The combined name is translated as "Boren's swift dicynodont" from the Ancient Greek argos ("swift", "quick") It was discovered in the Boren Quarry in the Tecovas Formation of Texas, strata which has also been referred to as the lower Cooper Canyon Formation, and is known from isolated remains of multiple individuals representing the skull, mandibles, vertebrae, pectoral girdle, forelimb and pelvic girdle.

The holotype specimen is a partial skull missing the front of the snout, palate and jaw joints, with a total length estimated to be 33 centimetres (13 in) long.

Argodicynodon was related to and resembled the well-known Placerias, but had a tall, narrow sagittal crest rising sharply from behind the eyes instead of a broad flat intertemporal region.

Unlike Placerias, Argodicynodon has prominent and exposed, but slender, tusks, more similar to the related Moroccan placeriine Moghreberia.

[1] The cladogram below depicts a reduced strict consensus tree of the relationships of Kannameyeriiformes from Mueller et al. (2023), with taxa that could not be over 50% coded for the analysis (e.g. the other placeriines Lisowicia, Pentasaurus and Zambiasaurus) not included:[1] Shansiodon Tetragonias Vinceria Rhinodicynodon Acratophorus Kannemeyeria simocephalus Kannemeyeria lophorhinus Dolichuranus Sinokannemeyeria Parakannemeyeria Xiyukannemeyeria Rhadiodromus Wadiasaurus Shaanbeikannemeyeria Dinodontosaurus Angonisaurus Ufudocyclops Stahleckeria Placerias Argodicynodon Moghreberia Sangusaurus Ischigualastia Jachaleria