How to get glue out of a necklace clasp?

Alright, so last night a necklace a friend gave to me broke. Since the beads have such small openings, the only thing that would work to hold it together was this really thin nylon/plastic thread thing for seed beads. Since this plastic thing has a tendency to untie knots, I had to hot glue the knots into the clasp, which to close you have to screw the two ends together. I left it overnight, and when I put it on this morning, apparently the glue wasn't entirely dry, because now it has glued it together. If I cut the wire, the ends will still be stuck inside of the clasp. So I am wondering, is there any way to get this to open without damaging the necklace too badly?