Define "abusive".
If it rises to the level of meriting a restraining/protective/stay away order, that's one way to get a person out...
If it's merely annoying, then check the terms of your lease to see if the tenant is violating it.
If it's merely annoying, but there is no lease, then you're an idiot. However, you can follow your localities rules and laws about how to terminate a tenancy-at-will.