meabeaver,
I don't know what hardiness zone you're in (your location info isn't showing up yet), but I'm in zone 6a, so my hibiscus is a 'hardy' perennial variety, ILO the tropical variety. So speaking from my own particular experience, I would say to remove all of the dead stuff and then snip off a bit from a larger branch. If it's green and moist inside, it's still alive and it will send up new shoots if you give it some tlc.
I don't know if you should cut it back necessarily. Perhaps another member can chime in here....
If you have the the tropical variety of hibiscus, I'm afraid that I can be of no help.
Good luck!!