Be sure your lather is slick. If it dries out and the blade is skipping across your face, you'll end up with that problem. Same if it's too wet and doesn't lubricate. If you use no pressure, proper angle, and good lather, you shouldn't get cut up. Is the blade gliding smoothly? If so, be absolutely certain of proper angle and pressure. If you never have trouble on a large, flat area you can easily see- say a cheek - try shaving that area first and pay attention to all these things. If something is wrong there, it's only going to get worse on areas you can't see as well or where you have a harder time with angles, etc. This should give you a good way to tell if the blade is skipping, tugging, at the right angle, no pressure, etc. If you're unsure, do both cheeks WTG and see if you can get better by the end of the second one.
If all is well there and you still have trouble, write back.
Daily driver: DE89, 7 OC Black, Palmolive Stick, FS Finest, Lucido/4711 mix or Nivea ASB.