Hi Gail The bolt that holds your toilet bowl down to the toilet flange should be brass (unless some unknowing person replaced it with a steel bolt :-( thus it should be soft and relatively easy to cut. If you cannot clean up the head of the bolt enough to tighten with a wrench or pair of vice grips, then you'll have to cut it off.
What I do is use my reciprocating saw on slow speed with a fine and long blade, lay it flat on the lip at the bottom of the toilet so my saw cuts the head of the bolt off flush with this lip. I do this on both sides, remove the toilet, replace the wax ring and replace the two brass bolts. Once installed, putting covers over them or even a dab of silicone will keep them from corroding so badly again in the future. If you don't have a recip saw, you can do the same thing, with a little more arm exercise, using a hack saw.
If you need some more help on this, visit your local plumbing store or the plumbing section of the big home improvement centers (like Home Depot). The plumbing guy there should be able to show you what I am speaking of.