Actually after looking at it again, I think you could frag a few pieces along the edge without too much problems.
Fragging the whole piece might not be so easy as I said before, the reason I say this, the disc on the Dremel will generally only cut about 1/2"-3/4" before it bottoms out on the arbor. Then you will need to crack it open the rest of the way and there is no guarantee which path the crack will follow.
OK, I've decided to go ahead with the fraging demo with the favia. I took a more recent pic with it out of the sand bed so that you can see what the whole thing looks like. I'd say it is about the size of a large grapefruit. And I'd like it to be much smaller so that it doesn't take up so much room in my tank..