It's not a mutation. It's actually a sign of his madness. Deadpool gained his powers through torture1, which mentally broke him.
Not only is he under the "illusion" (in-universe this is seen as a derangement) that he is a fictional character (his frequent 4th-wall breaks)
Ryan Reynolds has told Empire that he’s insistent on Deadpool‘s habit of breaking of the fourth wall to carry over from the comics to the big screen. That means, in effect, that Deadpool/Wade Wilson will sometimes address the audience directly, as with Ferris Bueller, say, or the character of Paul in Funny Games.
He also suffers from schizophrenia (voices in his head)2,
And while it could be attributed to the excessive amount of pain he undergoes on a regular basis - his reaction to pain and being mutilated over and over again is not one you would expect from a sane person.
1. In Deadpool 1, Ajax explains that the Weapon X program requires the body to undergo increasing amounts of stress in order to trigger the mutation.
2. This is in the comics, but not depicted in the movies. It is possible that this was tied into the 4th wall breaks as talking to the audience as the "voices" in his head