Like jetengine said, it's not enough to just be deranged or traumatized or whatever. You have to literally be so far gone that you can't comprehend what you're doing, what the consequences are or why you're being punished.
Joker running around doing things expressly to break people's spirit/sanity/sense of morality/etc. shows that he understands very well what he's doing and what the consequences of his actions are. He just doesn't give a damn.
Besides, I'm pretty sure Joker's just straight-up shot or stabbed people plenty of times.