I would definitely not remove the papers before sewing. The papers make the sewing and handling much easier.
I agree with the people that recommended the Fiskar's punch. The extra large one is 1", which is smaller than you want, but still very manageable, and you will save hours and hours of boredom and frustration with it.
I hand cut diamonds for my first EPP project, and cutting was thhe most time-consuming, least fun part of the process. I now use punches for hexagons, and buy all other shapes. This gives me lots more time for the fun part - the actual piecing!