Clinically, self-harm is grouped into different categories, but there doesn't seem to be one catch-all single-word term for it--just a collection of acronyms as outlined here from Wikipedia:
Self-harm (SH), also referred to as
self-injury (SI), self-inflicted
violence (SIV), Non-Suicidal Self
Injury (NSSI) or self-injurious
behaviour (SIB), refers to a spectrum
of behaviours where demonstrable
injury is self-inflicted. An
example of self-harm/self-injury is
cutting and is the second most common
form of self-harm in the UK. The
term self-mutilation is also sometimes
used, although this phrase evokes
connotations that some find worrisome,
inaccurate, or offensive.
I've heard people who cut themselves referred to, nonclinically, as cutters. Of course, the more specific you get in terms of what harm is being done, the more choices there are for clinical terms describing that particular compulsion, e.g., bulimia, anorexia, trichotillomania, algolagnia, etc. Then there's the whole realm of body modification, and a host of other specific terms like scarification.