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]
Old English heap "pile (of things); great number, crowd, multitude (of persons)," from West Germanic *haupaz (source also of Old Saxon hop, Old Frisian hap, Middle Low German hupe, Dutch hoop, German Haufe "heap"), of uncertain origin. The group is perhaps related to Old English heah "high" (see high), but OED suggests a common origin with Latin cubare "lie down," and Boutkan says it is probably not Indo-European at all.
Slang meaning "old car" is attested from 1924. Earlier it meant "slovenly woman" (1806). As a characteristic word in American Indian English speech, "a lot, a great deal," by 1832.
One grain of sand does not make a heap. A second grain of sand added to the first does not make a heap. Indeed each and every grain of sand, when added to the others, does not make a heap which was not a heap before. Therefore, all the grains of sand in existence can still not a heap make. [the fallacy of the heap, as described in Malcolm Murray and Nebojsa Kujundzic, "Critical Reflection," 2005]
mid-14c., junke "old cable or rope," cut in bits and used for caulking, etc., a nautical word of uncertain origin, perhaps from Old French junc "rush, reed," also used figuratively as a type of something of little value, from Latin iuncus "rush, reed" (but OED finds "no evidence of connexion").
It was extended to "old refuse from boats and ships" (1660s), then to "old or discarded articles of any kind" (1884), usually with a suggestion of reusability. Meaning "salt meat used on long voyages" is from 1762. Meaning "narcotic drug" is from 1925. Junk food is from 1971; junk art is from 1961; junk mail first attested 1954; junk bond from 1979.