That toilet should be able to be removed without disturbing the shelf return on the vanity top. Generally speaking the toilet only needs to lift about two inches to clear the hold down bolts. There is more than enough space below the shelf for that......and just in case it was not you can remove the tank cover to gain an additional 1.5 inches or so.
It is very likely polyester Fiberglas with a lot of limestone filler. It will cut fairly easily like hard wood ( and dusty). The cut face will be dull , the surfaces have a layer of gel-coat ( polyester) to give gloss. You can polish it some with sand paper.Sorry , I did not read the question carefully; the other answer is good.