i remove all corals from my tank for fragging, uless i accidently frag one in the tank (aka get clumsy and break one) just to keep extra pollutants out of my tank. I just siphon out a bucket of tank wtaer move the coral for fragging into it do the frag swish around let sit for a minute or to so it stops seeping. then return to my main tank. a little wont hurt but better safe than sorry. some corals pollute more than others when cut, torn, or snapped. I use all kinds of different tools from roto zips, to bone cutters to scalpels. fragging is easier than most think. if you do frag in tank I reccomend carbon.
also (since i realized you said you cant get it out) several water changes just after fragging would help, if you use amquell plus for pheremone reduction it may help (not sure on that note) but it probably wouldnt hurt.