I think if a student is openly doing something that is against the private school's code of conduct then the private school should be able to expel a student.
For example, if a private school has a policy against swearing then the private school has a right to expel a student. I would hope that if it was an accidental slip up, the school would give someone another chance. However, if it happens all the time then I think a private school should be able to expel for that reason.