Mutons represent the main part of the alien forces - a good, melee-oriented unit, where they employ their powerful attacks, capable of killing a soldier in a single strike. Additionally, they tend to use their plasma grenades, which can damage even 4 of your soldiers at the same time, taking up to half of their health bar in the early game. This is why you should always spread your soldiers when you are expecting to face a muton on the battlefield.
As mentioned, those unit seek to fight your units in melee range, where they definitely excel - aside from dealing immense amount of damage they are capable of stunning your units. Furthermore, they have a dangerous ability that allows them to perform a counterattack whenever they are stroke in melee - you must avoid doing so at all costs, as an enraged Muton can turn that into an instant death of your soldier.
Aside from that, they can use suppression fire, during which they are given a slight penalty to AIM, a huge boost to defense, and the suppressed unit that comes out of cover will automatically get shot at. The suppression ability is broken as soon as Muton receives any damage.
Lastly, Muton is one of the first enemies you stumble upon to have any armor, which is why you should open the encounter with a grenade, which will shred its armor, after which a single shot is often more than enough to bring the beast to its knees.