Hey Doug,
If it is really thick, use a Dremel tool and a diamond wheel bit. That's what I use. If it is thin, you can try using coral snips (bone cutters), but you run the risk of shattering the entire coral.
No Dremel? then try scoring the echino or chalice coral several times along your desired cut line several times on both side if possible, then snap the frag off when you feel you have scored it deep enough to not shatter the echino.