early 14c., "throw down or fall with force, drop (something or someone) suddenly," not found in Old English, perhaps from a Scandinavian source (compare Danish dumpe "fall hard," Norwegian dumpa "to fall suddenly," Old Norse dumpa "to beat").
The sense of "unload en masse, cause to fall out by tilting up a cart, etc." is recorded in American English by 1784. That of "discard, abandon" is from 1919. Economics sense of "export or throw on the market in large quantities at low prices" is by 1868. Related: Dumped; dumping.