Green’s Dictionary of Slang

(US milit.) a dishonourable discharge; thus the soldier thus discharged; also attrib.

1878		A.F. Mulford Fighting Indians 38: A bobtail discharge is one with the character clause torn off, and is considered the most disgraceful one a soldier can receive.
c.1880		‘O’Reilly’ [US army poem] They ran him in the mill, they’ve got him in there still, / His bob-tail’s coming back by mail, / O’Reilly’s gone to Hell.
1890		C. King Army Portia 272: Served with him at Fort Wayne until he got a ‘bobtail’ discharge.
1900		Star and Sentinel (Gettysburg, PA) 4/5: ‘Bobtail’ – A soldier discharged by reason of misconduct.
1907		C. M’Govern By Bolo and Krag 27: After we lands I tried me gol-darmnedest to get a bob-tail handed to me. [Ibid.] 28: The captain [...] couldn’t be took in by no enlisted man’s con game along the lines of stealing a bob.
1918		Wadsworth Gas Attack 12 Jan. 15: No More ‘Bob-Tails’ For Slackers.
1918		L.N. Smith Lingo of No Man’s Land 13: BOBTAIL, A dishonorable discharge, used more in the American army than in the British.
1921		Sentinel 14 Jan. 15: His bob-tail’s coming back by mail. 2: vt Discharge dishonorably or without honor.
1940		Phila. Eve. Ledger 20 July n.p.: ‘Bobtail’ – one who has been dishonorably discharged from the army.
c.1943		‘Bill O. Lading’ You Chirped a Chinful!! n.p.: Bob Tail: Dishonorable discharge.
1943		(con. 1860s) B.I. Wiley Life of Johnny Reb 343: As for fighting, few full-fledged Rebs expected that of ‘Bob-tail militia’ [...] ‘they ain’t worth a low country cow tick’.