Hexanchus agassizi was an early sixgill cow shark belonging to one of the most ancient surviving branches of modern sharks. Cow sharks retain a number of primitive anatomical features, including more gill slits than most living sharks, and their fossil record shows that the lineage was already diverse by the Palaeogene.

Its lower teeth formed broad multi-cusped cutting blades capable of slicing flesh, while other parts of the dentition had different roles. This feeding apparatus is consistent with an opportunistic predator able to tackle fishes and other vertebrate prey and, like living cow sharks, it may also have scavenged when carrion was available.

The species is usually represented by isolated teeth rather than skeletons, so its precise behaviour cannot be reconstructed. The dentition nevertheless indicates a powerful generalist predator occupying a very different feeding niche from the shell-crushing rays and slender-toothed sand tiger sharks of the same sea.