Is it possible to get addicted to cutting yourself?

Yes: "cutting" in the absence of suicide intent is due to some underlying conflict and/or feeling "numb" the most common reasons for "cutting" or other self abusive behavior are to feel more alive or to punish oneself. Cutters often describe a feeling of relief or escape from reality in much the same way as using drugs.

Definately: People cut for a variety of different reasons. Cutting can allow someone who feels numb or empty to feel something. Cutting can cause physical pain which acts as a distraction from emotional pain. Some people use cutting as a form of self-punishment. Some people cut as a cry to help. Others may cut to let out evil humors. Cutting may be used as a coping mechanism (not a very healthy one).