Someone bothering the community should be banned or suspended.
That’s simple enough.
If the individual creates new accounts or otherwise continues attacks on your community, you need to go further to resolve the issue (note resolve, not revenge).
Collect evidence of their activities and present this evidence to their ISP. Most ISPs have terms of service that prohibit spamming, harassment and otherwise being a plague to other individuals.
If a member keeps coming back, or makes remarks that are racist, incites hatred, or threatens other members, contact the police.
Don’t play the cat and mouse game. Don’t keep repeatedly banning a member.
Resolve the issue efficiently and move on.