To defeat Cut Man, shoot him as he comes within range. He is one of the Robot Masters who gets knocked back when he gets hit. At the first hit, stand close to him, then he would either jump or throw his Rolling Cutter at you, which acts like a boomerang. It is best to stay far away from him as possible, then shoot him from afar. Keep him away by knocking him back with the Mega Buster. Jump over his Rolling Cutter then sniping him is the most effective strategy against him.
Cut Man is weak against the Mega Buster, but he is weakest against Super Arm which you will obtain if you defeat Guts Man beforehand. In Cut Man's room you have only 2 blocks to use with Super Arm & you must hit him squarely with those to defeat him with just 2 hits.
Cut Man is also weak against Fire Storm, which you will get if you defeat Fire Man beforehand. However, it has the same power as Mega Buster, which deals 3 points of damage.
In Dr. Wily Stage 2, you will encounter him again for a rematch. There are no blocks to use with Super Arm, so use the first strategy to defeat him.
Cut Man appeared in every episode in the cartoon version of Mega Man. He has orange ears.
Cut Man only appeared in Mega Trouble in Megaland and looked very different the Captain N version.