Demonstrate your ability to control the cow and keep it from getting back to the herd. Keep one hand on the saddle horn and hold the reins in your other hand. Guide the horse with leg pressure. Cutting horses are quick and agile and if you're not careful, they could be going in one direction while you're going in another. Win with the highest score.
Judges score a rider and horse on their ability to maintain proper position with the cow.
Horses move from side to side, swinging both their front feet from the left side to the right side, never moving their hind legs at times. Cutting can be dangerous. Sometimes the horse moves in one direction and the rider moves in the other and falls off. Cattle are unpredictable. Normally they'll just run from side to side but occasionally a cow will try to charge you and your horse.