The genus is monotypic, known only from the type species Gorgodon minutus from the Early Permian of the southwestern United States.

Gorgodon was described and named by paleontologist Everett C. Olson in 1962 from the San Angelo Formation in Knox County, Texas.

He placed it in the family Phthinosuchidae because its teeth seemed similar to those of Phthinosaurus, an enigmatic therapsid from the Middle Permian of Russia that is most likely a dinocephalian.

Sidor and Hopson (1995) proposed that Gorgodon and several other early therapsids that Olson described from the San Angelo Formation were instead the crushed remains of sphenacodontids.

[2] Sphenacodontids are a group of non-therapsid synapsids that were common in what is now the southwestern United States during the Early Permian.