Yes, take it to a local mechanic or maintenance mechanic. They would drill a small hole in the center of the broken piece and remove with an easy out. If the break isn' t clean and it has a lip on the broken stud, have somebody hold the bow for you. Take a small punch or screwdriver and line it up on the broken lip and tap gently with a hammer to unscrew the stud(counterclockwise). If you do this its important to do it gently so you don' t mess up the threads or your bows riser.
Also you could try to drill a small hole in the center of the broken stud with the drill in reverse. Sometimes the bit will grab and unscrew the stud. Again be careful because the drill bit may want to wander and do damage to the riser.
Good Luck
Dan