I have taught. This possibility has been toyed with before--at least in the minds of teachers with dangerous students and an indifferent admin bureaucracy.
The targets of the suit should be the students and parents, though--suing the school system just dumps on innocent taxpayers.
If a student can be tried as an adult in criminal cases, why not in civil? And upon a defaulted monetary judgement, perhaps an injunction against attending class be enforced instead. Expulsion by lawsuit...?
Incompetent parents regard the school system as a holding tank for their little thugs. Kick the punks out. What's so hard about this?
Students sure don't hesitate to sue the teachers. Turn it around.