As someone who was bullied for the better part of his early school career (kindergarden to grade 6) i'm going to have to say that if a group of kids cant understand that gang beating someone is wrong, they deserve to be put in a special school.
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".
The police don't have the authority to remove a kid from school without jailing them. The school administration is empowered to provide sanctions and have experience and training in dealing with children. It's a very different game than the police who deal with adults, using Tasers.
And the thug says "What do you mean, 'the next time you do XYZ'? I never did XYZ! If he says I did that, he's lying!" And since the third parties to the abuse are other kids who don't want to have reputations for being snitches, the thug can continue to abuse with impunity.
Kids are really good at low-level social dynamics. They know the balance and go with the flow. That's how bullying often is so successful. For a bully, only limiting factors are fear of punishment and disapproval by peers.
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?
I'm far from an expert, but that was naive. You missed that part about bullies often having problems in school, didn't you?
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.