First off, what the hell is a "natural grip"? Every pitch, fastball or not, has a different grip. There is no "natural grip", unless you're suggesting anything other than a four-seamer is not a fastball.
Secondly, you don't alter your motion on a cutter. It's a two-seam fastball. You place your fingers across the laces and pull with your finger tips as you release, which causes the cut at the end. Sliders, sinkers, knucklers, and even some change-ups are altered deliveries/hand motions. I would argue that a splitter and a cutter, you throw with the same force and arm/wrist angle as a fastball. The placement of the fingers and the pressure is what causes the movement.
Feel free to correct me if my assessment is wrong.