1803, "to cut off in lumps," from junk (n.1). The meaning "to throw away as trash, to scrap" is from 1908. Related: Junked; junking.

New settlers (who should always be here as early in the spring as possible) begin to cut down the wood where they intend to erect their first house. As the trees are cut the branches are to be lopped off, and the trunks cut into lengths of 12 or 14 feet. This operation they call junking them; if they are not junked before fire is applied, they are much worse to junk afterwards. [letter dated Charlotte Town, Nov. 29, 1820, in "A Series of Letters Descriptive of Prince Edward Island," 1822]