Cut Man
Cut Man is early in the route since the nature of his stage does not give opportunities to save time with other weapons. He is also Elec's weakness, and we want to visit Elec soon for Magnet Beam, but the Elec Buster fight is a pain.
Early Screens
Cut Man
If you fight Cut Man in Wily 2 instead of zipping, the buster fight strats will be relevant.
Buster Fight
Get onto ground level and fire shots at Cut Man. Don't let him get close. When he fires the rolling cutter, jump over it.
There are strats for grabbing the Stage Clear Orb faster, usually involving iframes and jumping up the unused guts blocks.
Guts Fight
If you are doing Cut Second and have Guts Man's Super Arm, you can use the blocks in the left corner.
You can hit Cut Man with the thrown block directly, or with the scattered debris. You can also select glitch the scattered shot to hit twice if desired.