Say a student was insulting another or some individual. If the remarks aren't categorized as a death threat, would the "bully" be suspended? Also, what if this was a case of Cyber Bullying, where the problem didn't occur on school grounds? Does a school administration have the jurisdiction to punish students who make insulting remarks on the internet?
In the United States, education is largely handled by the States. A similar, but broader question, concerning suspensions is this one by jimsug. In it, you'll find a helpful compendium of U.S. student disciplinary laws.
As an example, Illinois recently allowed suspension for bad behavior via electronic means.