i dont' know what you mean about the string slicing, but the strumming takes a bit of practice, and it's really hard to pick up jsut buy watching him do it.
the way i do it i bring my middle finger up against the meat of my thumb in the palm of my hand and go down and flick the finger downwards, then for the upstroke bring it back into the palm of your hand, it should be a relaxed easy motion. getting the accuracy is the hardest part. but if you're playing double stops or chords then it's not much of an issue. others may use first finger, i prefer middle. but once you can do one you can any, other than maybe the pinky.