Major,

That cutting will soon diminish as you hone your skill with the straight razor. The best way to avoid it now is to take your time and shave slowly while paying strict attention to keeping the proper angle and applying no pressure.

Also, try not to choke the blade in your hands by holding an iron grip on it. Think of the razor as a bird: that if you squeeze it too hard, it will perish, and too light, it will fly away. This will also help you maneuver the blade better.