The Muton has a 66% chance to negate incoming melee attacks. If it does so, it automatically performs a Bayonet strike on its attacker.
Incidentally, Counterattack all by itself is a good reason to consider Dominating a Muton, as the AI doesn't 'see' Counterattack and so is perfectly happy to fruitlessly hurl a bunch of melee attacks at the Muton, no matter how many Chryssalids break their teeth on the Muton's arm. Conveniently, Mutons are disproportionately prone to showing up alongside melee enemies, as they're particularly common on Retaliation missions and can outright be following around Berserkers. It's not like the rest of the Muton package is a bad deal, either, and their poor Will makes it pretty reliable to pull off, even with poorly-trained Psi Operatives.
Alien Grenade
Throws an Alien Grenade, doing 4-5 damage and 1 Shred to all units caught in its blast radius.
Unusually for explosives, this has the default +1 chance of 50%. It thus averages slightly higher damage than a Plasma Grenade used by your own soldiers, if we ignore skills like Volatile Mix.
As with ADVENT Troopers and Officers, this grenade has a notably larger radius than your own grenades have by default, enough so it can be surprisingly difficult to avoid multiple soldiers being caught in the blast radius. Otherwise, it's essentially a slightly weaker Plasma Grenade -which makes sense, since Mutons are visibly carrying a Plasma Grenade, and Autopsying them is how you unlock Plasma Grenades- and the extent to which it's slightly weaker (1 less Shred) isn't very important, as your own access to Armor is much lesser than enemy forces: aside a SPARK with fully upgraded chassis with the Bulwark skill and Sacrifice currently active, hitting a total of 6 Armor, player Armor is mostly going to be in the 1-2 points range. If you commit to Armor you can get as much as 4 points on a regular soldier: 2 from a W.A.R. Armor, 1 from Blast Padding, and 1 from equipping a Plated Vest. At that point Alien Grenade only having 1 Shred is almost like a real disadvantage... but the game isn't particularly rewarding of Armor stacking, and in fact is so oriented toward the best defense being everything dying before it can attack you that a Plated Vest is usually going to be a waste of an equipment slot and Blast Padding an iffy expenditure of Ability Points.
The main thing worth noting about Alien Grenade is, as I've noted before, that Mutons are, for whatever exact reason, really prone to responding to Panic by charging your squad and chucking their Alien Grenade at the squad. Outside of when they're Panicking, Mutons only rarely toss their grenade, in part because of their obsession with melee: there's a surprisingly narrow distance at which a Muton can't melee anyone but can lob their grenade. Quite often they'll either be too close, and go for the Bayonet strike, or be too far, and so not have the option of lobbing the grenade.
That said, if a Muton does remember its Alien Grenade, it's basically guaranteed it will vaporize all the Cover of whoever it gets thrown at. If any enemies are able to follow up, that can be quite lethal. As such, Mutons are a moderately high-priority target.
On a different note, I recently worked out why enemy grenades have a larger blast radius than yours, except Purifiers: because originally, they didn't, but one of the handful of patches base XCOM 2 got nerfed explosives all-around for the player, including shrinking their blast zone, and apparently the devs just didn't patch enemy explosives to be consistent. Meanwhile, Purifiers got introduced well after this patch, so they got the same radius your Incendiaries have post-patching.
Kind of a weird result...
Suppression
A single enemy target in range becomes Suppressed until the start of the user's next turn. A Suppressed target suffers -35 to Aim, and if it moves the Suppressor will immediately take a reaction fire shot at the target for free. Additionally, if the target was on Overwatch, its Overwatch is permanently removed, even if the Suppression ends prematurely. Suppression ends if the reaction shot is triggered of if the Suppressor takes damage. Consumes 2 ammo to initiate. No cooldown.
Just like on Mecs, Suppression on Mutons is generally a waste of their turn. The waste is a bit less egregious: for starters, Mutons being so focused on melee opportunities means they're less prone to even considering Suppression in the first place, and for another while it's still worse than a regular shot Mutons are more prone than Mecs to ending up in a situation where all their options suck or are unavailable. A Muton that can't get in range to melee, can't flank, and has no great Alien Grenade targets deciding to Suppress one of your soldiers in High Cover is probably a waste of their turn, but if their only other option is taking a shot that's unlikely to hit... well, that's not nearly as egregious as a basic Mec ignoring its Micromissiles to Suppress, or getting a flank and Suppressing instead of shooting.The other good news is that this is the last Suppression-capable enemy in XCOM 2. Suppression is terrible in XCOM 2 still, but at least it wasn't passed out to literally half the enemies like in the prior game.

Mutons are both familiar and yet quite different, mechanically. They're still an early-midgame Alien that falls away in relevance once you've got end-game weaponry on everyone, they still have access to Suppression and an Alien Grenade, but they've lost the largely-pointless Blood Call and the irritatingly random Intimidate in favor of leveraging their hulking mass and tribal history notions to become a fairly threatening melee combatant. (Which incidentally makes Berserkers a little less unnatural) Thus; familiar-yet different. (Also they have Shred on their gun, but this generally doesn't really matter)
On a different note, Mutons are one of the best enemies in the game to set on fire, particularly in War of the Chosen where a lot of enemies that were previously hard-disabled by fire now ignore it aside the damage. Mutons are, after all, one of the only enemies where taking a shot is one of the least threatening possibilities for them to do -it's more threatening than Suppression, admittedly, but most of the time locking off Suppression is worth doing as part of locking off Bayonet, Plasma Grenade, and of course Execute. And remember: enemies can't Hunker Down, and don't get Medikits or the like, so unless water happens to be present they can't put it out.
Overall, the main element of Mutons worth mentioning is how they fit into a larger design trend in XCOM 2.
In the prior game, the overt mechanics were clearly designed under the idea of the player closing with the enemy, between flanking bonuses and the Aim climb most weapons experienced. Unfortunately, this was in actual practice pretty consistently punished by the game; sure, you got Aim climb for getting closer, but so did the AI, and the way Aim/Defense math is tuned in that game a given amount of Aim boost is usually more valuable to the enemy than to the player.
In short: the AI tended to have worse Aim than the player, and Aim boosts have a greater proportionate impact the worse your Aim already is, taking into account how Aim intersects with Defense. A unit with 50 Aim firing on a unit in Full Cover would have a 10% chance to hit. Get close enough to get +20 Aim, and that chance triples to 30%. Meanwhile, a unit with 70 Aim is going from 30% to 50%, which is less than doubling your chance to hit. Which means a low-to-mid-level player unit facing off against a Floater where they're both in Full Cover should optimally just... sit there and keep exchanging fire, rather than trying to get in the Floater's face for the Aim bonus.
This is very possibly the reason why XCOM 2 removed Aim climb from AI units, incidentally. I'm not a fan of it as a solution, but I can kind of see how they arrived at it as an idea, given the above problem.
But this was far from the only way the prior game punished what it was intended to reward. Flying enemies of any sort exacerbated the issue by making it impossible to flank them if they didn't want to be flanked, while they were free to flank the player; thus, getting closer to them was making it easier for them to flank you with no equivalent reward on your end. Sectopods, Cyberdiscs, and Ethereals all exploding meant that getting closer could be punished even if you never let the enemy have an actual action. Melee enemies removed the 'Aim climb is more useful to the AI than to the player' factor, but replaced it with 'distance completely removes their ability to hurt you', which is actually even more extreme about encouraging keeping your distance. Grenades were another widespread incentive to keep your distance, being one of the only ways the AI could 100% reliably force damage on your units, where the only defense was to be too far away for them to toss it at your soldiers in the first place. And of course pod activation mechanics meant that anytime you advanced on enemies you were risking adding enemies to the fight when your goal was to subtract enemies from the fight.
XCOM 2 hasn't removed all these mechanics, but it's put a fair amount of effort into making the default behavior of the game be that approaching the enemy is actually rewarded, instead of punished. The introduction of powerful, useful melee attacks to the player's own arsenal being one of the more obvious examples of such. (Yes, I know Mecs had the Kinetic Strike Module in Enemy Within. It didn't do as much to encourage getting in close as you might hope)
Then we have XCOM 2 Mutons, who are a rare exception to this XCOM 2 trend: with most enemies, you should very much default to closing with them. With Mutons, it's generally better to keep your distance. I actually like that, as it helps make Mutons feel very different from many other enemies. They're not actually the only enemy you're encouraged to keep your distance from (Purifiers are another big one, in War of the Chosen), but they're probably the most dramatic one, and they're one of the better examples of XCOM 2 being better at setting up enemies so you approach fighting different enemies in a fundamentally different manner, instead of everything being fought basically the same regardless of its capabilities.
Mutons are, in fact, probably my favorite enemy in XCOM 2 from a design perspective, contrasting with Mutons in the prior game being one of my least favorite. It's a pleasant surprise.
Autopsy-wise, Mutons are a really big deal, directly unlocking the Advanced Grenade Launcher and the Plasma Grenade Proving Ground Project. Not only does the Plasma Grenade Project replace your Frag Grenades with superior Plasma Grenades, but it unlocks the Advanced Explosives project, which permanently improves not only all your Experimental Grenades but also your EMP Grenades! (And technically your Smoke Grenades, though that... barely matters...) As such, they're strongly worth considering Autopsying early, instead of ignoring entirely or waiting for the Instant Autopsy to be reached. This is compounded by them being a sufficiently uncommon enemy it's not at all unusual for you to never reach the instant threshold.
Furthermore, in War of the Chosen the Muton Autopsy is actually necessary for Powered Armor -which is nice, actually tying into the idea that Mutons are supposed to be wandering around in their own powered armor, a concept the previous game claimed but then didn't do anything to support. Mechanically, this pushes their Autopsy even further into importance, more or less tied with the ADVENT Mec for importance in the long haul. It's not unusual for me to Autopsy the Muton first, in fact, depending in part on what all I'm doing with the run. (eg a SPARK-heavy run gets less out of the Muton Autopsy, whereas if I've ended up with multiple great Grenadiers the Muton Autopsy is fantastic)
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Narratively, the game is... a bit mixed-up when it comes to Mutons.
The talk-y bits are in fairly consistent agreement that the XCOM 2 Muton design is new from an in-universe standpoint, heavily implying the design from the previous game is canonically the form Mutons took in the initial invasion. Some late-game cinematics also depict previous-game Alien designs, Muton included...
... such as this shot during the first Codex Shadow Project cinematic, depicting Muton Elites, Mutons, Ethereals, Heavy Floaters, Outsiders, Sectoids, Cyberdiscs, and Chryssalids, all in their design from the prior game where its relevant to note the distinction. All of which implies XCOM 2 is taking the position that the current design is not a retcon, but a change in-universe.

Nonetheless, if you have the Tutorial on there's a flashback toward the beginning of the game that depicts an XCOM 2-style Muton breaking into X-COM's base.
Mind, there's a lot of choreography problems with the Tutorial cinematics...
Also notable in this regard is that Bradford's introduction to Mutons describes them as seeming 'a little more agile' than the Mutons of the prior game, which is confusing as XCOM 2 Mutons don't have any new mechanics that could be argued as growing out of greater agility. They're not faster, they don't suddenly climb more widely, they don't have any of the new Dodge stat... I honestly have no idea why this is a thing Bradford says. Is it supposed to somehow be a warning of their newfound melee capability, just with an absolutely baffling choice of words?
The whole thing is sufficiently messy I'm honestly not sure where to start for theories on why we ended up with this confusing set of decisions.
In any event, the visual design itself... exists? I don't really get why they got redesigned like this, personally. I had issues with the prior game's design, but some of these have already been addressed by shifted mechanics, such as how this supersoldier in powered armor has an actual Armor stat and dominates your puny human soldiers in melee. The new design admittedly moves away from the 'space gorilla' design to something a bit more alien-looking, but the Alien designs are still slanted toward Suspiciously Humanoid so there's not much of a believability gain there. The redesign itself raises questions, particularly with it being acknowledged in-universe that they look different; I was more positive on the redesign when I was first playing, when it seemed like they were taking the All Just A Dream reframing of the prior game as an opportunity to redesign everything. With it being clear that, no, the older designs are still canon... whyyyy did the Muton get this redesign? From both an out-of-universe standpoint and an in-universe one, it's baffling.
What's particularly confusing is that Mutons are one of the enemy types that's allowed to show up on maps with ADVENT civilians. If Mutons had been redesigned into something more PR-friendly, I'd get it, but if anything they seem more intimidating and evil-looking now, making it weird.
I do at least pretty unambiguously approve of the removal of Blood Call. Its mechanics were terrible, the racial unity thing didn't make much sense -as I've said before, there's no logical reason why Mutons exhorting their comrades would only affect members of their own species- and it wasn't that interesting in practice. My only mixed feeling is that a better implementation of it would've actually been consistent with XCOM 2's implementation of complicator enemies.
In general, while I approve of the mechanics overhaul for Mutons, I'm just baffled by the narrative/visual elements.
Oh, and they still have their gasmask, it still doesn't have any mechanical implications, and they're still not protecting their head. In fact, their head looks more vulnerable now, because it's much larger and sticks a fair distance forward whereas they no longer have the oversized collar to potentially protect their head from most non-front directions.
I love their gameplay end, particularly in War of the Chosen, but I just don't get the rest of what happened with them.
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See you then.