Nosaj 
While blocking is a good tool, if you're using the web interface I also recommend Reporting egregious breaches, both to your local moderation team (the default report) and also forward the report to the instance the perpetrator is on (an additional checkbox on the web interface).
This allows for the both your moderators and the other servers moderators to be made aware of the bad behaviour of the user. To be fair, your moderation team probably can't do much about the user on another server, but they can monitor the other server's response to the bad behaviour. If the other server takes no action, that is a statement in itself.
Community responsibility builds better communities. Blocking so you can't see them doesn't stop the underlying problem, which is the problem user.