What are you cutting into below the print? I use the large Alvin cutting mats whenever I am cutting a print, RC, fiber or Matte paper. This material give the blade something to bite into and won't dull the blade. You can get the mats in many different sizes. The ruler I use has a small strip of foam that helps to hold the ruler on the print and won't damage the face of the print. Any good hand held blade should work fine on the cuts.
For cutting foam core before mounting a print I always use a Fletcher wall mount, mine is the 48" inch version they also make a 60". You can trim foam core down very easily this way. I always cut my foam core before mounting the print. So if I am working on a Print that is 23 x 33 which I will mount and mat to 30 x 40, I will cut the foam core to 30 x 40 first, place the print with the mat, then do the dry mount. There are many ways to do this, this works best for me.
Paul