Is it normal for your mouth to get cut from...

That's weird. And probably not good for you

My friends, boyfriends, braces cut up her mouth once .. But not everytime.. Be more careful or stop kissing him? Wait... How exactly were you kissing him? Ah, nevermind. I don't wanna know.

Not real normal..

My braces would cut me too especially when u get hit in the mouth area with something like a hand while playing football then it really digs in.

My braces used to cut me. Maybe their the old fashioned kind with lots of wire sticking out.

I don't thin that's normal. That has never happened to me. But maybe ask him to put the braces wax on it beforehand?

No. Not normal. Braces aren't sharp. You're doing it wrong.