Usually you don't.
I'll keep the plug itself, as it's inert rock and it makes mounting the coral infinitely easier. Depending on where I plan to mount the coral, I will sometimes cut off the stem with a pair of bone cutters, giving me a flat surface to press up against the rockwork with the glue/epoxy sandwich.
The biggest challenge with polyp-type corals (zoanthids, for example) is getting them to attach to something. The frag plug solves that problem, so I don't look to actively give myself that problem.
For a stony coral (whether LPS or SPS) it's a bit different. I'll still usually leave them on the plug, but if you want to remove them it's not as big a deal since the coral will actually stick to glue. If you do want to remove the coral from the plug... bone cutters are still probably the answer. A high-speed cutter (usually a Dremel or a coral saw) can also be used to cut the frag off the plug, but most people don't have access to one of those and it's usually overkill.