Does the head of the pin sit on any sort of lip inside the caliper? If it does, you're going to have a hard time unthreading it from the other side, even if most of the head is gone. If I was in your shoes, I would probably try what you're thinking of, since it looks like it might be the last thing that you can try. I would try and cut the pin so you have as much of it as possible still attached to the caliper, and I'd try and file a flat side on each side of the pin. That should give a set of vise grips a better purchase on the pin. And I would soak that thing with something like PB Blaster for about a day. If the head of the pin isn't sitting on some sort of recess in the caliper, I'd take it out from the rear of the caliper with the vise grips. If there is a lip there, then thread it into the caliper from the back side, and hopefully you can thread enough through to be able to grab the pin from the other side and unthread it the rest of the way.
"No matter where you go, there you are."