Yep mirrors and lizards are problematical, we had a large wild (male) water skink visit inside the house who reacted very violently when I placed a small vanity mirror on the floor against the wall, he spotted the "other lizard" almost immediately and charged up to the mirror , headnodded violently then attacked it so fast I could hear the loud bag when he collided with mirror.
He only stopped attacking it when the mirror fell over and wound up under him, at which point he lost interest and left .
Your beardie likely knows the "other" beardie in the mirror is himself or not really there, when his hormones kick in you'll likely have a much more vigorous and violent response when he see's his own reflection , he's likely to become very aggressive towards "that other male".
I recommend against housing two beardies together unless it's to mate them (and then only to let them do the deed) , central bearded dragons are NOT SOCIAL , and do better housed separately.