Cherie, Love the picture!
In answer to your question, no. If you try to use it without the mat or on a selfhealing mat, it will tear your paper!
I have the 8x11 mat and a bigger one I think 11x14. (I ordered them from crazy scraps) They are so inexpensive, you may as well do it right! I bought a couple of coluzzle on a whim (50% off) and have enjoyed using them for something "different".
Have fun! Kathy