A laceration or cut was a type of deep tissue injury.
Captain Jonathan Archer suffered from a bleeding cut in his lip which he received during his interrogation by Andorian Commander Thy'lek Shran in June of 2151. (ENT: "The Andorian Incident")
In the 23rd century, in the medical history section of Christopher Pike's personnel file, a laceration was listed with other ailments he had suffered during his lifetime prior to 2257. (DIS: "Brother")
Lieutenant Immamura suffered severe lacerations as part of a second landing party which beamed down in search of missing crewmembers on Taurus II. (TOS: "The Galileo Seven")
In 2364, Beverly Crusher coached Jean-Luc Picard on first aid as he helped her avoid shock after suffering multiple lacerations from a fall into a pit on Minos. (TNG: "The Arsenal of Freedom")
Patterns in lacerations and tissue damage could offer forensic clues as to an explosive's nature. In 2367, Beverly Crusher found these to be almost impossible to detect in dead Klingons after a bomb blast. (TNG: "Reunion")
In 2371, The Doctor treated Fred Noonan's lacerated carotid artery, caused by weapons fire. (VOY: "The 37's")
In 2373, Kira Nerys suffered a placental laceration after being felled by the exertion of attacking two Bajoran deputies, but both she and the unborn baby were fine. (DS9: "The Darkness and the Light")
In 2374, Tom Paris, deputizing for The Doctor, treated Seven of Nine's lacerated carpal nerve. (VOY: "Revulsion")
In an alternate timeline that year, a blinded Tuvok cut himself shaving which he described to Seven as "a minor laceration." (VOY: "Year of Hell")
Later, The Doctor admonished a Hirogen medic to be more thorough when treating muscle lacerations. (VOY: "The Killing Game")
In 2376, Maxwell Burke examined Seven on the USS Equinox and told her she had first-degree phaser burns and minor lacerations. (VOY: "Equinox, Part II")