Normal Mutants are one of the most common enemies in the game, and they don't pose much of a threat, unless there are a lot of them.
The normal mutant will just run toward the player and lunge when it gets close, attacking with its hands. West will be slowed for a second if this attack lands (unless his shield blocks it). You can avoid its attacks by strafing, or by dashing away from their attacks. Normal mutants are only remotely dangerous in numbers, but they can still be outrun easily.
Any weapon can easily dispose of these, but a well-placed shotgun blast to the face will instantly kill a mutant, regardless of difficulty. There is a noticeable cooldown between their attacks, so getting close is not too difficult, and is good practice for the evolved melee mutants that will eventually appear. A Plasma Launcher is not recommended; normal mutants are one of the fastest enemies, so a careless shot can easily hit West, as well.