On slippery fabric, I put a few pins along the selvage to keep that lined up. I have all the material supported on the table. I fold the fabric to fit my large cutting mat. I place my large 15 inch square on the fabric to help hold it square and flat. I carefully cut along my long ruler and move the square as I go also. I have found that on slippery fabric, I must not move the fabric at all so I make sure it is all folded up on my board before starting to cut. Maybe someone else will have better tips for you.