A cutting beam is a beam of directed energy which is used to perform a cutting function.
A cutting beam was generated by a phaser-like tool used by Starfleet engineers in the 2260s. An engineer used such beam to free Scotty from the jammed core hatch in 2269. (TAS: "Beyond the Farthest Star")
Borg starships are known to have the ability to generate cutting beams of great power, strong enough to slice sections of a starship, or even a planet, open with great precision. In conjunction with the Borg tractor beam, their cutting beams are used to "scoop" pieces of ships or cities for assimilation by Borg drones and collectives. (TNG: "Q Who?", "The Best of Both Worlds, Part I & II).