Английский Этимологический словарь - sap (v.)

- "wear away," 1598, originally "dig a trench toward the enemy's position," from M.Fr. saper, from sappe "spade," from L.L. sappa "spade." The sense of "weaken" is first recorded 1755, and was probably influenced by the notion of "undermine" as well as by the verb form of sap (n.) in the sense of "draining the vital sap from."