It depends on what penalties, and the severity of the student cheating.
So, the student is cheating on something minor, something unimportant, then I don't think they need to be kicked out of class just for that, but maybe get a 0 on that whole thing and that will teach them a lesson.
If the student is cheating on something important (excluding big tests), then the school should probably: A, give them a 0 on it or B, move them down to a lower level so the student feels like they don't have to cheat.
The worst thing they could do is cheat on a really big test like an exam, then they will probably end up with a big fat 0 on it all and flunk that class, or get kicked out of class.
Lots of people (adults and kids) think that penalties should be easier on the kids, but I don't agree with that. If the kid has done something wrong, then the kid needs to pay for their actions and deal with the consequences.