If a student is really "bad" they get punished by being kicked out of the school system permanently. In the US, when a student is expelled from a public school there are legal defenses s/he may call on to appeal the decision because public education is a legal civil right.
Before a student is expelled they may have been suspended many times or had multiple incidents of rule breaking documented. A student may also be expelled for a "first offence" if it is considered serous enough.