There are other forms of crazy that also motivate self-cutting. Some forms of dissociative identity disorder include strong feelings of being fake, as in not a real person. One might think they are a robot or an animated manikin or similar. Of course this sounds unrealistic (and unlikely) to most of us because we don't experience this. But for people who suffer these episodes, they are extremely disturbing.
So they cut themselves to see their own blood. It helps alleviate the anxiety of the condition. Seeing their own blood helps ground them in their sense of being an actual living creature. Apparently, feeling the pain can help with this too. Though if episodes are lengthy, one cut isn't enough, because the blood dries and resembles plastic, which adds more fuel to the fire.
On a different spectrum, as I understand, there is "sympathy-seeking" cutting, where people cut themselves so their injuries will be seen by others who will then offer support and sympathy and attention. Our society tends to take a pretty dim view of this one, seeing it as mere selfishness or immaturity. Which it may be, in some cases. But in cases of extreme feelings of isolation, loneliness, rejection, etc., the emotional imbalances are enough to drive on to depression and suicide, so it can actually be indicative of a serious condition, and a legit cry for help.
I have read about religious cutting as well, as in "stigmata," where a person internalizes an expectation that this should be happening to them (from their religious upbringing) and experiences cognitive dissonance when it doesn't happen for too long, and wind up doing this to themselves with only semi-awareness so they can then surprise themselves at the discovery of the injury mere moments later.