I use a dremel tool, with a diamond tip wheel. I just cut a thin layer of rock away, and use a small flathead screwdriver to "po" it off the main rock. This leaves a nice base to glue down.
Or, you can take the zoos out, get them all closed up as tight as possible, and take a scalpel or thin blade hobby knife, and cut out a section that you want to frag. You will have to outline the section, making sure you cut completely through the mat, and then "peel" the mat off of the rock. Just use whatever you cut the mat with to get underneath of it. It sounds like you are just ripping it apart, and in a way you are. This will give you a clean mat to either glue down, or to allow it to attach itself.
I always try to take mat cuts from the center of the colony. The colony tends to produce quicker when I do that, as opposed to just taking from the edge.
My palys don't have the mat like my zoos, and I apply the same concept when fragging them, just get underneath of the polyp, and pry it off of the rock or plug.
I glue mine down with a super glue gel.
Some others might have different methods, but this is how I frag.
I hope this helps.