The Catalogue of Life doesn't list Puna as a genus, so it's no longer a genus, and Puna mandragora apparently is a highly obsolete species name because it isn't even listed as a synonym of any other species in any of the major taxonomic databases.
If you're going to chase down an ID for your plant, Lindsey, I might have a starting point for you. Most of the Puna species became species of Maihueniopsis. There once was a species called Maihueniopsis mandragora, but it's now a synonym for Maihueniopsis glomerata.