Originally Posted by FBinNY

Let's start off with the basics. Generally you remove the entire brake via the nut in the back (towards front of bike on the rear brake) before servicing it. Now, grab the remainder of the center bolt with a pair of pliers and remove the nut with a 6mm hex key.

If it's rusted in place, use a 6mm or larger drill (1/4" is fine) and drill straight down the remainder of the center bolt until you pierce the back and the bolt spins on the drill. Then push the nut out the back. If you don't have a drill, you can saw through the bolt as close as possible to theframe, then file the rest off until you can push it out.

It's also possible to drill through the nut until the flange falls off, but this can be more difficult since you're forced to drill at an angle. Work from both sides, and try to drift the drill up and down to weaken the flange as much as possible, then work or punch the center bolt through.

BTW- I have a bunch of new centerbolts if your brake is otherwise in good shape, or depending on reach needed, I have a wide assortment of NOS calipers I can offer you cheap.