I have never ripped fabric, although I have seen it done on videos. I carefully fold and then cut, and I usually have good results.

I check to see if the print is straight - then I cut one layer at a time - moving the cutting mat under the uncut portion - or sliding the fabric along the mat - whichever works better

Probably not the quickest or most efficient way - but if my cutter slips - it's usually only a little nick on one section -