This is highly subjective to start. Each case varies highly. But schizopherenia could cause violence, but not directly. It would probably be caused by severe delutional states (imagining a loved one is actually a snake trying to kill you), hallucinations, and severe anxiety.
Bipolar could as it is a sudden shift in mood, and when someone with bipolar disorder suddenly shifts to manic they could possibly hurt someone.
As for general mental illnesses, there are so many, its like asking "will being sick give you an intense fever?" its a possibility, but depends upon the sickness and the person in question.