I'm pretty sure that either can cut themselves.
My understanding is that many of the reasons that people start cutting could apply to anyone - bipolars included.
People who have trouble talking about their feelings may show their emotional tension, physical discomfort, pain and low self-esteem with self-injurious behaviors. Other factors identified include:
Relief from psychological/Emotional pain.
Release of tension.
Inability to handle feelings, good or bad.
A history of physical, emotional, or sexual abuse.
Cutting isn't usually the problem, but a way for the person who is cutting to deal with the problem.
(Ok, everyone wants to know whether I cut? Actually a year ago there was a girl on the Mental Health Board who was a cutter and I looked some of this up so I could understand a little better)