I had a lot of trouble with that when I started cutting, as well. The basic problem, at least for me, was technique. I had to practice a lot with keeping the cutter blade totally vertical, and lined up perfectly with the ruler. The problem I (and I suspect most people) had with moving the ruler was canting the cutter in against the ruler, like this /| while the blade should be straight with the ruler, like this || as well as being perfectly vertical. When I switched to a Martelli Ergo cutter it helped a lot too, as it eliminated the "flop" in the cutter.
Of course, I had an advantage in that my wife is a "certified rotary cutting instructor" and she taught me how to do it correctly.
:mrgreen:
It takes some practice. Get some old cheap Wally fabric and practice a lot, cutting strips. The non-slip stuff you got works well too!