What is the punishment for receiving a seruv from a Bais Din for litigating B'Arkoas (in non-Jewish courts) without a heter?
A search found the following on the consequences of a shtar siruv:
2) Rabbinical Court of Greater Cleveland Feb 2005. The named person is subject to the strictures of Yoreh Deah 334 (2).
I did not find how these were applied practically.
Are you asking how G-d punishes it? I don't know.
As far as what we can do today, today's batei din don't have the power of corporeal punishment. (Israel is a bit more complicated, let's assume we're talking elsewhere.) Depending on the language of the seruv, the rabbis could call on the Jewish community to shun the individual; deny him any honors in synagogue; or potentially even bar his entrance to synagogue altogether. Shulchan Aruch discusses different levels of bans, some of which would mean the individual can't even count for a minyan. Rabbenu Tam is famous for describing an agreement that no one in the Jewish community would do business with someone found in contempt; my understanding is this is rarely used today (but I heard Rabbi Hershel Schachter state it might be necessary to bring it back).
In short, it can vary, and it only works based on how people in the local community agree to abide by it. If the fellow under contempt walks away from the community altogether, well we live in a liberal society and there's little we can do. (Though we could still assemble peaceful protests on public land outside the guy's house, for instance.)