Green’s Dictionary of Slang

(Aus.) of an animal, worn out, thus worthless; also as n.

1899		‘Steele Rudd’ On Our Selection (1953) 6: The horse was an old ‘tuppy’ mare that Dad used to straddle.
1957		J. Greenway ‘Australian Cattle Lingo’ in AS XXXIII:3 169: tuppy, n. A worn-out animal.