Your bug is from the order Neuropter, family Mantispidae - the mantidflies. There are only 18 species in the USA, mostly in the South. There are 6 species in the arid Southwest. They are between 20 and 35 mm in length, so not too tiny.
They are predatory-parasites. The adults are generalist predators of small insects. The larvae are parasites and are known to parasitize spider egg masses, subterranean larvae of Scarabeidae and Noctuidae, and certain social wasps.
Very cool critter that seems to not be well studied. Perhaps someone wanting to get their PhD should consider working on these guys!