First, you should use a dictionary, google translate is not reliable.

extirper most common meaning:

to pull out, take out, whip out (remove something from e.g. a holder, pocket, holster etc.)

EDIT: It is often used to express that the action was not that easy to pull out.

and for mutilation:

The act of mutilating or the state of being mutilated.

Therefore, mutilate:

• To physically harm as to impair use, notably by cutting off or otherwise disabling a vital part, such as a limb.
  To destroy beyond recognition.

To conclude, “extirper” will be about removing something and could be a way to mutilate, (and cause “mutilations”) but can also be a way of healing or just an act that has nothing in common with damaging [some]body.