How do I remove a stripped plastic nut?

I am trying to remove a toilet seat that is cracked but the plastic nut holding the bolt on is all torn up so I can not get a grip on it with pliers. Is there an easy way to remove this or should I think about trying to saw through the bolt?

I always used a reciprocating saw and cut them off I used duct tape to protect the porcelain its tougher. A hacksaw is hard to do it with because you will be cutting on an angle,if you dont have a recip. try a narrow blade jab saw. Done it a lot of times,easiest way.

Use a flat tip soldering iron to melt a groove in the nut.
Never hammer on anything touching a porcelain toilet.

If you plan on keeping the toilet consider my reasons about do or dont's. Its your toilet try whatever method you like. lol
Otherwise turn off the water & whack it near the bolt with a hammer Wala! your toilet seat is now off.
1st choice is dollar store ect wood burning tool with knife tip or soldering iron. This method will stink open a window.
*Do not use a propane torch directly on bowl ! However you might heat a spike nail in vice grips or a junk screwdriver.
2nd Carefully use rotary tool with burr,
3rd not really choice hot air gun will soften/ maybe melt it however may crack bowl because of contrasting temps.
4th Most drill body prob wont fit anyway DO NOT drill blind from above you may chip the bowl. Some plastics are slippery, melt & get stuck / bond on drill bits.
5 th I personally wouldnt hammer a chisel it will most likely slip off the round plastic & chip the bowl.
6 th Finally if possible use metal toilet bolts.

Spray WD-40 on it first before you try removal of the bolt it will make the task 10 times easier

This can be a bear. If it is recessed into the flange area, then cutting the bolt can be the quickest way. If not, I have used a very sharp wood chisel and have cut the plastic nut away. Either way, the job can get done.

Good luck!

Being plastic and in a place hard to get to, you might find it easier to cut the nut rather than the bolt.

Just to check: Are you holding the bolt still with a screwdriver? OK, then try pulling down on the nut while turning and see if you can grab good threads. You can cut it off with a hacksaw blade under the hinge. I'd put masking tape around the area to try to keep from scratching the porcelain. Also, you might try hollowing out the bolt with a bit that's just smaller and see if you can snap it off.