Green’s Dictionary of Slang

(US) as a euph. for root n.¹ (1a), the penis.

1920s		‘Root, Hog, or Die’ in G. Logsdon Whorehouse Bells Were Ringing (1995) 140: I had a notion in my head, cowpunching I would try, / Never thinking what I’d do about my root, hog, or die [...] We got our shaves and baths, and then struck out to try / To see if we could find release for our root, hog, or die [...] I went to piss, my asshole was on fire, / And I had a dozen shankers on my root, hog, or die.
1943		in Randolph & Legman Ozark Folksongs and Folklore (1992) I 581: I went to the doctor and told him I was sick, / The first thing he said was, Let me see your prick. / I showed him and I saw him as he winked his eye, / He said, You have the shankers on your root hog or die.