Originally Posted by FBinNY

If the bolt ends below the depth of the slot in the nut section, you can remove the crank. stand a screwdriver up in a vise, and push down on the crank to keep the screwdriver in the slot while turning the screw out with a hex key.

OTOH, keep in mind that chainring bolts are pretty damn cheap, and not worth sacrificing tools for. If it persists in it's stubbornness, use a 5/16" drill to drill it through and both halves will come out their respective sides. Then pay the $2.00 and buy a new bolt.