I'm about ready to kick this customer out of the restaurant I work at.
What is he doing to warrant being kicked out?
He's arrogant and expects me to wait on him personally to the exclusion of everyone else in the restaurant.
Well, in general you shouldn't kick a paying customer out, at least not without the boss's approval. However, if they're truly being unruly, you should get rid of them. That behavior affects the other paying customers, and they may leave.
I'm always the one with the dirty section on the grill and he is really rude about it.
I am sorry you are dealing with that. You should talk to your boss about kicking him out or at least getting another server to wait on him.