To have one of your enemies "Green River" you was definitely not a good thing to happen to you back in the days of the Old West.
This expression (one of those "Westernisms" I've featured here from time to time) meant you had been stabbed, probably very deeply and most likely with a fatal wound, with a large knife -- originally with a Green River knife. This knife was extremely popular in the early days of Western exploration and settlement, becoming well known as the Mountain Men and other fur trappers and traders brought them into wilderness territory for everyday use cutting, skinning, and preparing animals for food.
(It's worth remembering here, we aren't talking about modern kitchens, where perfectly nice Western replica cutlery will do the job. We're talking about a time when sturdy men used sturdy knives to rip apart large animal carcasses -- as well as carefully skinning off the fur or hide for clothing and to make a living.)
The origin of the knife and especially its name are not clear. But my two most reliable source on Westernisms, "Dictionary of the American West" by Winfred Blevins and "A Dictionary of the Old West" by Peter Watts, agree that the name Green River had nothing to do with the river and later town in Wyoming of the same name. The large, sturdy knife of that name was around considerably before the town was named.
It appears that the knife, described as a "heavy knife" and accompanied by a sketch in Watts' work, may have been brought into the West by members of the Hudson's Bay Company and marked with a "GR" standing for Georgius Rex (i.e., King George of England). Mountain Men who used the knife decided "Green River" should be linked to those initials instead of the British monarch, and hence the name "Green River knife." (Both Watts and Blevins are skeptical about that story, but admit that it makes a great tale.)
Blevins and Watts agree that the most likely origin of the Green River knife's name was that the originals were manufactured by knife maker John Russell in his factory on the Green River in Massachusetts and were brought to the mountains of the West in 1840s. The first knives made by Russell were very high quality and extremely valuable among trappers and explorers of the day -- which soon led to counterfeit knives that took advantage of the GR engraving and the Green River knife name, and which were inferior to the originals.
It appears that the original and early models of the knife had the "GR" initials near the hilt of the knife, and that led to expressions like "Green Rivering" someone -- stabbing them deeply up to the initials on the knife! The related expression, to "go up Green River," became a euphemism for "to die."
Not all uses of the expression were so grim, however. If someone were very zealous and dedicated in doing a job, people might say they were working hard, "up to the Green River," as in -- they're working "up to the hilt," or putting their all into the effort, or going all the way.