Earlier quoted context omitted.
You expel them and they become another person's problem. I heard recently of a local problem child aged seven. He's already been expelled from a private school but has entered a state school where he seriously injured another pupil and attempted to strangle one of the teachers. Expulsion isn't going to reform them, it will just move it on elsewhere.
No this is not true. Expulsion works in many cases. The idea of getting expelled prevents a lot of problems. A lot of people avoid doing things that will get them expelled but this of course doesn't apply to everyone including the person in your example. It's similar to how prison is a deterrent to crime. But it doesn't change the fact that there are people who still do crimes and get into prison.
They may be bullies themselves because of an ongoing toxic culture in the school. That can include the teachers in some cases, who are some of the worst bullies in there. I had one who persecuted me for a speech impediment and humiliated me in front of an entire class of children by making me say tongue twisters.