Turbinaria reniformis. Easily fragged and glued but grows very slowly and for this reason is not farmed much (I think). Bigger frags with as many polyps as possible do best. It is very hardy and interesting. Adds a very nice contrast to SPS dominated aquascapes.
I think you can just snap them off and you'll have a nice frag, like any other coral, although I'm not sure if they are more sensitive to being broken than others.
Thanks for the responses. I think I will try the hacksaw method (as archaic as it sounds). I think am going to chop a large piece off of the main colony and attaching it to some rock instead of chopping it directly in half.