I'm posting the TBI info that lumps both songs together:

Whoa Mule (The Kickin' Mule)
DESCRIPTION: The singer describes courting and the dangers of a kicking mule which "kicked the feathers off a goose," etc. The stubborn mule Simon Slick is often mentioned. The chorus will generally contain the instruction "Whoa, mule."
AUTHOR: unknown
EARLIEST DATE: 1924 (recordings, Bill Chitwood & Bud Landress, Sid Turner)
KEYWORDS: animal courting talltale humorous
FOUND IN: US(Ap,MW,SE,So)
REFERENCES (6 citations):
BrownIII 513, "The Kicking Mule" (1 text)
Scarborough-NegroFS, p. 186, "Whoa, Mule!" (1 text, 1 tune)
Brewster 84, "Simon Slick" (2 texts, longer than most, 1 tune)
Lomax-FSNA 231, "The Kickin' Mule" (1 text, 1 tune)
Pankake-PHCFSB, pp. 62-63, "Whoa, Mule, Whoa" (1 text, tune referenced)
DT, SIMONSLK*
Roud #3774
RECORDINGS:
Roy Acuff, "Whoa Mule" (Capitol 2738, 1954)
Clarence Ashley & Tex Isley, "Whoa Mule" (on Ashley01)
Loman D. Cansler, "Kickin' Maud [or Kickin' Maude]" (on Cansler1)
Bill Chitwood & Bud Landress, "Whoa Mule" (Silvertone 3050, 1924; Brunswick 2811, 1925)
Al Clauser & his Oklahoma Outlaws, "Whoa, Mule, Whoa" (Melotone 7-08-63, 1937)
Elisha Cox, "Whoa Mule" (AAFS 547 A2)
J. D. Dillingham & O. J. Light, "Whoa, Maude, Whoa" (AAFS 899 B2)
Samuel Clay Dixon, "Whoa, Mule, Whoa" (AAFS 1749 B3/1750 A1)
Leonard C. Fulwinder, "Whoa Mule, Whoa" (Aurora [Canadian] 238, c. 1932)
Georgia Yellow Hammers, "Jonnson's Old Grey Mule" (Victor 20550, 1927); "The Sale of Simon Slick - Pts. 1 & 2" (Victor V-40069, 1929)
The Hillbillies, "Whoa! Mule" (OKeh 40376, 1925)
Hinson, Pitts & Coley, "Whoa Mule Whoa" (Bluebird B-7438, 1938)
Paul Holland, "Whoa, Mule, Whoa" (AAFS 3217 A1)
Al Hopkins & his Buckle Busters [or John Hopkins], "Whoa, Mule" (Brunswick 179, 1927)
Matilda Keene, "Whoa, Larry, Whoa" (AAFS 979 B1)
J. E. Mainer's Mountaineers, "Johnson's Old Grey Mule" (Bluebird B-6584/Montgomery Ward M-7006, 1936)
Bert Martin, "Whoa, Mule" (AAFS 1479 B2)
Chubby Parker, "Whoa Mule, Whoa" (Gennett 6120, 1927; Supertone 9189, 1928) (Conqueror 7892, 1927)
Pickard Family, "Thompson's Old Gray Mule" (Oriole 1502/Challenge 990, 1929; Conqueror 7736, 1931; Broadway 8179 [as Pleasant Family])
Riley Puckett, "Johnson's Old Gray Mule" (Columbia 150-D, 1924); "Whoa Mule" (Columbia 15040-D, 1925; Silvertone 3258, 1926)
Prairie Ramblers, "Jim's Windy Mule" (Conqueror 8648, 1936; Vocalion 03587, 1937 [as Sweet Violet Boys])
Pete Seeger, "Old Grey Mule" (on PeteSeeger08, PeteSeegerCD02)
Hobart Ricker, "Whoa, Mule, Whoa" (AAFS 3904 B4)
Shelton Brothers, "Johnson's Old Gray Mule" (Decca 5161, 1935) (King 646, 1947)
Roba Stanley [or Stanley Trio] "Whoa! Mule" (OKeh 40271, 1925)
Gid Tanner & his Skillet Lickers, "Johnson's Old Gray Mule" (Columbia 15221-D, 1928); "Whoa, Mule, Whoa" (Bluebird B-5591, 1934)
Sid Turner, "Go 'Long Mule" (Perfect 12147, 1924)
Tom Watson [pseud. for Gid Tanner & Riley Puckett], "Johnson's Mule" (Harmony 5095-H, n.d.)
CROSS-REFERENCES:
cf. "Going Down to Cairo" (words)
Notes: Every version of this I've heard sung uses the Lomax chorus, "Whoa, mule, I tell you, Miss Liza, you keep cool; I ain't got time to kiss you now; I'm busy with my mule." It doesn't seem to show up much in tradition, though (it is found in the Brown text in a slightly different form). - RBW
Trying to sort out "Whoa, Mule," "Johnson's Old Grey Mule," and related songs is Excedrin Headache #1927. We've lumped them for want of a better solution.
This shouldn't be confused with a fiddle piece, "The Kickin' Mule," made popular by Fiddlin' John Carson; that one has a different tune. - PJS"