if a Mage of Mind has violent tendencies (due to being a purple blood like Gamzee) that they're trying to express in a healthy way without actually hurting anyone, how would they be able to do so through their Mind powers?

That is an… Extremely specific question. Also ‘violent tendencies’ and ‘healthy’ don’t tend to go hand in hand. I really do not think a Mage of Mind’s powers could channel something like that? Unless they were fighting their literal inner demons within their mind and beating the crap out of anxiety and fear, but still. That’s… Yeah.