You say to the thug, in no uncertain terms, "The next time you do XYZ, the consequences will be a removal from school." And, yes, have the police deal with it because they are actually equipped for such activity, unlike your typical teacher.

...and to be clear, I'm talking about instances of actual assault, and not the vast bulk of things in the category "bullying".

If making bullying a legal case is the only way left to proceed, any parent should just go ahead, and take it as far as necessary. Sometimes it's just the school administration who need a kick in their collective ass to actually do something about it. At the far end, it's the bully himself who is in need of that kick.

You are assuming that somebody wants to make things out of proportion. Is it out of proportion, for example, to call police if your kid has been beaten or robbed on the way home? You can't be seriously claiming that to protect the fragile worldview of the thugs/thieves you should sacrifice the one of the victim?

Generally, you want to stop the bullying for one of the same reasons you want to stop rapes -- it damages the lives of many victims. But you also want to catch this, because the bully often needs help.

Edit: I don't really have an opinion on when/if the police should get involved. It probably depends on bow fscked the teacher subculture is.