The story
First use appears c. 1929 as a noun, most likely from the nautical cry by the deep six indicating a depth of six fathoms (36 feet, 11 metres) as measured by a sounding line (a depth at which something thrown overboard would be difficult to recover), though possibly also a reference to the common depth of graves (six feet). Attested since the 1950s as a verb.
Etymology from Wiktionary, CC BY-SA 4.0.