Screw bit broke in screw

[quatin]

So I was putting on a clamp mount on a rifle and while tightening the screws, the bit (allen screw) broke off in the screw. There's a 1/10'' sticking out, but not enough for me to pull it. Normally I would take a hammer and a nail and hit it until it comes loose, but the clamp is still attached to a scope. How does one go about removing this? I just want the screw off the clamp so I can get my scope back.

 

[dfariswheel]

Use a small hammer and a very sharply pointed punch, (NOT a soft nail) and very gently tap the broken Allen wrench on the sides.
DON'T just hammer on it, use gentle taps.

What you want to do is tap around the broken piece so you rock it from side to side.

This will usually allow you to gradually move it up out of the hole.
If this doesn't work, you'll need a PRO machinist or gunsmith to drill the head off the screw without damaging the mount.,

 

[Clipper]

If you have a drill press, you can drill it out from the back side with a smaller (than the minor screw diameter) drill. Usually, the drill will engage the screw shank during the process and drive it out. Use a padded drill vise, or a v-block to hold the work steady!