Baissabrenthorhinus mirabilis was named by Legalov (2015). Its type specimen is PIN 4210/5921, an exoskeleton, and it is a compression fossil. Its type locality is Baissa (PIN collection 4210, unknown layer), which is in an Aptian lacustrine - large siltstone/marl in the Zaza Formation of the Russian Federation. It is the type species of Baissabrenthorhinus.