Schele De Vere, Americanisms (1872), p. 200:
A very odd expression, confined, however, mainly to the mountaineers in the wilder parts of the Southwest [...] they say they send a man up Green River when they have killed him. The phrase had its origin in a once famous factory on Green River, where a superior kind of large knife was made, very popular among hunters and trappers. On the blade the words 'Green River Works' were engraved, and hence the mountaineers, using the knife to despatch an adversary, literally sent his blood up Green River.