Is it ever possible to do surgery on a joint that will not stop bleeding?

Hemophilia? Why the knee bleeds? If there is a compelling emergency to fix the knee physicians may try to give fresh frozen plasma during the procedure; if the bleeding is due to hemopnilia the specific factors must be given or at least cryoprecipitates. Consult witha hematologist. No physician will risk surgery during and posteriorlynto surgery unless they knowmtheyncan stop the bleeding.
YES. Lots of reasons a joint bleeds- but it is important to stop it, and sometimes surgery is the best way.