Dissection was the scientific procedure of taking something apart to study it.
In 2154, Doctor Phlox criticized K'Vagh and Antaak for bringing him a live subject for dissection rather than a dead one. K'Vagh complied by shooting the ill Klingon. (ENT: "Affliction")
In 2267, Commander Kor threatened to have Spock dissected, as well as James T. Kirk turned into a mental vegetable, through use of the mind scanner. The following year, Nyota Uhura asked Leonard McCoy not to tell her if he planned to dissect one of her tribbles. McCoy promised not to harm it. (TOS: "Errand of Mercy", "The Trouble with Tribbles")
In 2365, when Wesley Crusher solicited advice on how to approach Salia, he responded to Data's remarks on their compatible physiology by saying he wanted to meet her, not dissect her. (TNG: "The Dauphin")
In 2366, Commander Tomalak told Jean-Luc Picard of his plans to dissect the USS Enterprise-D to retrieve information. (TNG: "The Defector")
Later that year, Geordi La Forge wryly commented that the Romulans would probably dissect Gomtuu instead of studying the creature. (TNG: "Tin Man")
The following year, Jono hyperbolically complained that Beverly Crusher was trying to dissect him. (TNG: "Suddenly Human")
In 2371, a paranoid Neelix asked The Doctor if he could scan or dissect Ensign Michael Parsons after the officer changed his drink order uncharacteristically. (VOY: "Cathexis")
In 2373, The Doctor suggested performing a submicron dissection on Borg nanoprobes as an attempt to discover the assimilation mechanism. (VOY: "Scorpion")
In 2374, The Doctor performed every conceivable neural analysis on Kes' brain short of dissecting the brain itself. (VOY: "The Gift")
In 2376, an overwhelmed Seven of Nine suggested that Kathryn Janeway planned to bring her back to the Alpha Quadrant just to be dissected to gain intelligence on the Borg. (VOY: "The Voyager Conspiracy")