Yes the foam mat is the cutting mat. I really like mine, but it does take practice to perfect the cutting technique.
Here is a link to their cutting instructions.
http://www.coluzzle.com/products/col...ns&cl=coluzzle
Coluzzle Tips
The coluzzle is very easy to use. Some tips to make it easier for the beginner:
1. Lay the pad on a flat surface, with nothing underneath it.
2. Be sure and hold the swivel knife STRAIGHT up and down while moving it through the template opening. You do NOT hold it slanted like a regular knife!Sometimes standing up and looking down as you cut will help you keep the knife straight. Keeping the knife straight is the key to perfect Coluzzle cutting!
3. Do not pick the swivel knife up until you hit the plastic piece, then put it on the other side to continue to make the rest of the cut until you hit the other plastic piece.
4. Be sure and hold your paper in place, so that it does not move and ruin the cut.
5. When you open the templates, they have a plastice covering on them that you must remove. I try to get in the corner and peel it off from there. It is on both sides of the template.
6. Make sure your blade on your swivel knife is screwed in tightly. If it is not, you will be nicking your template like crazy.