[2] The genus was named by Edward Drinker Cope in 1881 as a member of the Acreodi, a now invalid taxon that encompassed creodonts, mesonychians and certain arctocyonians.

The mandibular body of T. crassicuspis is proportionately deeper dorsoventrally and significantly more robust compared to that of Eoconodon coryphaeus, or mesonychids like Sinonyx jiashanensis and Dissacus praenuntius.

The teeth of Triisodon exhibit several morphological similarities to those of other triisodontids including the diagnostic characteristics of the group: basin-shaped talonids and tribosphenic upper molars.

Other features of the teeth reveal that Triisodon and other triisodontids were showing evolutionary trends towards a carnivorous lifestyle – notably the mesiodistally oriented hypoconulid crest, tall trigonid and distinct protoconid of the lower molars, as well as the strongly-developed posterior premolars bearing marked shearing surfaces.

The radial diaphysis is also rather straight in its proximal portion, with a bicipital tuberosity that is proximodistally long, but not particularly prominent compared to condylarths including G. levisanus, Ar.

Triisodon also had a massive, hemispherical femoral head with a smooth articular surface, and an ovoid, somewhat deep fovea capitis for attachment of the ligamentum teres.

[5] The molars of Triisodon are very much unlike those of modern specialized carnivorans in being wide, brachydont and bunodont, comparable to those of ursids, inferring a diet comprising seeds, nuts and fruit, as well as carrion, Triisodon potentially had a large bite force for engaging in durophagy or to compensate for unspecialized dentition, as evident from the robust molar cusps and the deep mandibular fossa.

The fossa for the abductor pollicis longus muscle on the ulna suggests high-powered forelimb extension, which is movement possibly linked to brief bursts of quick terrestrial locomotion including running.