late 12c. as a surname, "one who cuts" in any sense, "one who shapes or forms by cutting," agent noun from cut (v.). From 1630s as "instrument or tool for cutting."
As a type of small, single-masted vessel, from 1762, earlier "double-banked boat belonging to a ship of war" (1745); perhaps so called from the notion of moving quickly, or of "cutting" through the water.
Revenue cutter, a light-armed government vessel commissioned for the prevention of smuggling and the enforcement of the customs regulations. Formerly the vessels for the protection of the United States revenue were cutter-rigged, but now the name is applied indiscriminately, although almost all the revenue vessels are steamers, and the few remaining sailing vessels are schooner-rigged. [Century Dictionary, 1889]