Technique, luck... We all get small cuts from time to time, but the Mach 3 is an outright face mangler compared to a straight.
Follow Lynn's tip, start small, and build your comfort level.
It took me 2 months of shaving cheeks and sideburns before I was ready to try my chin, and another 3 months before I could get my chin reasonably clean.
all in all about 10 months before I was both competent and confident enough to chuck my Mach3 in the bin.

I still get cuts, or weepers when I get too agressive, (usually on my chin) but as long as I keep my razor sharp, it isn't painful.
I could dry shave with one of my straights and still get less irritation than I did from my mach3, or from an electric for that matter...