S. mirabilis is known from a unique holotype specimen, which was first described by Aleksandr Grigorevich Sharov in 1971.[2] Sharov named the species Podopteryx mirabilis, "foot wing", for the wing membranes on the hind limbs. However, that name had previously been used for a genus of damselfly, Podopteryx, so in 1981 Richard Cowen[3][4] created the new genus name Sharovipteryx for the species.