Reddy's tips will work...
one of our other members said with the thinner papers she usually tapes another piece of cardstock over top of the pattern piece that is directly on the mat....and cuts them..thus giving the pattern paper a cleaner cut...
So, your pattern paper goes on the mat like you would normally cut it... add the other piece of paper on top of the pattern paper..tape it down on the edges with masking tape than cut like normal (especially is you would prefer not to adjust the depth of your blade). Make sense??? I usually use the white papers that come in between page protectors in an album.