how to break a bead with a hammer!
I've had this problem with carbon rims that have a bead-lock ridge to keep the bead seated. It's great for keeping the bead from unseating if you flat or loose enough air during a ride, but yes, it makes it a PITA to remove the tire.
Here's what I've found to work best when all else fails:
1. deflate tire but leave enough air to provide some side wall support (this is key)
2. lie the wheel on the ground and put both knees on the tire and rim at about 6 o'clock
3. take a hammer and press the base of the handle on the tire as close to the bead and rim as possible near 3 or 4 o'clock (if right-handed)
4. press down HARD on the head (anvil) using your weight to collapse the bead (be sure to hold the hammer vertical and not let it slip!)
5. as soon as one section breaks away, flip the wheel over and break the bead on the other side 180° away from the first bead break.
6. after one section breaks loose it's fairly easy to push the rest to the center channel
This method seems to work well because it applies high force to a small area. The wood base of most hammers has a good enough edge to get close to the bead near the rim but it is much less likely to damage a tire than using something sharp like a screwdriver. Sometimes I have to adjust air pressure to get the right amount of resistance in the tire so the sidewall will help support the hammer base.
In an emergency on the trail I would search for a short thick stick or equivalent to use as a substitute for the hammer. Fortunately, I haven't had to do so yet. A cut or tear that prevented the tire from holding any air would make it tough!