I tried to use my gladiator gryphon to fight in the arena, he has no energy but the gladiator bar is full (in 10). I thought he could use the energy in the gladiator bar to fight.

Is this a bug? if not please explain. Thanks!

It's not a bug. Your Gryphon must have energy both for wins and losses to enter arena. Otherwise his energy should become negative in case if he wins.