With zoas, use a razor blade/exacto knife and cut between the polyps, then use the blade to carefully cut under them between the rock/plug they are on and the base. Once you have them cut off put a dot of super glue on a frag plug and stick the zoas to it.
Mushrooms, they spread fast enough on their own. You can cut them in pieces, making sure to get a piece of the center on all parts you cut, and it will regrow, but never actually known anyone to do that because they grow fast enough.
Brain coral.. I wouldn't attempt it, but usually a band saw is the method of cutting/fragging those then dipping in something like iodine to stop infections from setting in. Brains, scolymias, fungias, all those large one giant mouth LPS corals scare me to frag.