Sometimes I use a wet saw or cutters depending on the rock and sometimes I scrape them off with a scalpel and throw them into a dish of rubble or just glue them directly to a plug.
When adding them to the tank, I like to glue a small frag piece in place, wait for them to attach and grow onto the rock and then pry the frag back out and put it into the frag tank. That way if something happens to either piece I have a source to replenish it.