Imhotep can create sandstorms and huge tidal waves, but only if there is a supply nearby like a desert or a lake. He can reassemble himself if his limbs are torn from his body. He can turn himself into sand or a localized sandstorm. He was shown to have superstrength, telekinesis (he lifted that kid), and can shoot bugs from his mouth. His only weakness is the Book of the Dead.
Mumm-Ra can fly, has superstrength, can project energy from his hands and eyes, teleport, and change his shape and size. His weaknesses are that he has to regenerate in his sarcophagus after an undetermined amount of time. Lion-O defeated Mumm-ra by throwing this sarcophagus in that pool of liquid in front of it. It should also be noted that he always gets someone else to fight the Thundercats in his place, is he scared or lazy?
The Book of The Dead and Mumm-Ra's sarcophagus do not exist in my arena and therefore can not be used. Imhotep's sandstorm and bugs are no use against Mumm-Ra since he can Teleport away or blast the bugs. There is no body of water, except for a pool in the neighbouring school, or desert for Imhotep to control so he is limited to his other powers. Mumm-Ra's energy projection won't be able to kill Imhotep but maybe just hurt him enough to give him pause. I am assuming they are equal in hand to hand combat and strength. I thought about Mumm-Ra maybe trapping Imhotep beneath the ruins of the school by giving it a huge blast but Mumm-Ra doesn't seem to me as the type to think of something like that. I am not sure if that would hold Imhotep since he could just turn into a sandstorm and get out of there. I think they would just fight until Mumm-Ra's time limit is reached and he turns back into his more feable form. This form may have some powers but they were probably already exhausted from the fight. I think this is a win for Imhotep by default (a first for my arena) or maybe we can say that Imhotep finds a way to kill Mumm-Ra in his weaken state.
Winner: Imhotep