"place where something is discarded," by 1921 (in phrase give (something) the deep six), originally in motorboating slang, perhaps from earlier underworld noun sense of "the grave" (1929), which is perhaps a reference to the usual grave depth of six feet. But the phrase (in common with mark twain) also figured in the sailing jargon of sounding, for a measure of six fathoms:
As the water deepened under her keel the boyish voice rang out from the chains: "By the mark five--and a quarter less six--by the deep six--and a half seven--by the deep eight--and a quarter eight." ["Learning the Road to Sea," in "Outing" magazine, Feb. 1918]In general use by 1940s. As a verb from 1953.
To dispose of, discard, or get rid of: “The board of directors deep-sixed the proposal without even reading it.” This phrase is derived from the noun “deep six,” meaning burial at sea and referring to the depth of water necessary for such a burial. The term was later used as slang for a grave (customarily six feet underground) and, by extension, as a verb meaning “to kill.”
A grave (1920s+ Underworld)
To discard; jettison; throw overboard: One White House disposal crew even unblushingly planned to deep six a file in the Potomac/ If any publication is deep-sixed, it will almost certainly be ''The Car Book'' (1940s+ Nautical)
[probably fr the combined notions of a grave as six feet deep and a fathom as six feet in depth]