Does masturbation cause acne?
This is another example of "If two things happen at nearly the same time, does one cause the other?"
A boy generally doesn't masturbate until he starts producing semen. He doesn't produce semen until he starts changing from a boy to a man. Typically semen begins to be produced either in stage 2 or stage 4 -- about half the guys start in stage 2 and the rest in stage 4.
Acne begins showing up as a side-effect of growth. The body produces too much oils which has a tendency to clog the glands. Acne starts to appear in stage 3 and gets worse in stage 4 before it starts settling down.
In other words both masturbating and acne are both results of the fact that a boy's body is changing, but neither causes the other to happen.