A scalpel was a medical tool used to create incisions. Considered crude by 24th century standards, their function was usually taken over by laser scalpels.
Doctor Phlox kept scissors, scalpels, and tweezers in a box in his sickbay. In 2151, he used the tweezers to place litmus paper on a slide. (ENT: "Civilization")
The Cardassian Doctor Crell Moset preferred using a scalpel in his surgeries, as he believed that more advanced implements "removed" doctors from their subjects. (VOY: "Nothing Human")
In 2268, James T. Kirk told Leonard McCoy that wishing away scientific advances made by man was like the doctor wishing that he still operated with scalpels. (TOS: "Return to Tomorrow")
In 2367, the phasers of the USS Enterprise-D were used like a scalpel to excise an infant spaceborne lifeform dubbed Junior from its deceased mother. (TNG: "Galaxy's Child")
In 2372, The Clown created a scalpel in his virtual reality to invoke Harry Kim's traumatic childhood experiences. However, The Doctor corrected the positioning of The Clown's index finger in order to attain "optimal dexterity." (VOY: "The Thaw")
In 2374, when The Doctor had trouble identifying a thrombic modulator, the EMH Mark II on the USS Prometheus sarcastically informed him that science had made advances while he was in the Delta Quadrant and that scalpels and leeches were no longer used. (VOY: "Message in a Bottle")
In 2376, when The Doctor tried to explain to Lewis Zimmerman that he was trying to treat him because he cared about him, Zimmerman replied that he was not programmed to care, he was programmed to hold a scalpel. (VOY: "Life Line")
In 2377, Iko held Seven of Nine prisoner in the USS Voyager's sickbay with a scalpel to her neck. (VOY: "Repentance")