How should I go about "reseting" a large arena?

You could use the /clone command, with one clever difference: You have two arenas, and while one is /cloneing, the other would be used.

This may cause major lag, though. I don't know; try it.

If you would like to actually reset the map in-game, you could use the /fill command (Preferably in command blocks) to set all the blocks back to normal and get rid of any fires, etc. and use the /kill @e to kill all mobs (Do /kill @e[type=creeper,Zombie,Skeleton] and etc. to kill only the mobs you spawn and not actually you). You could use additional /setblock commands for any areas not on the certain y-axis (1 strange block on the 105 y-axis, while the rest of the arena is on the 104 y-axis).

The fill command: /fill x1 x2 x3 y1 y2 y3 BlockType

If, though, you would like to use the hidden files (%appdata%) and create backup files of the arena you could do that too, but that would probably not be possible in your situation.

Hope this helped! If you need further information make sure to comment and I will answer it! :D

Using scoreboards, you can track the placement of blocks and do a local clone of that area, but I don't know the command itself; the only reason I know it exists is because a Youtuber used it to make Zelda bombs here, but really with a space that big the only good way to replace that many blocks is to do it with individual command blocks, if the games lasts a while I would build 3 instances, 1 that you use for the cloning, and two for playing on, like ratchet freak said, that way you can continue playing another game while the command blocks work on repairing the first game you played, other than that you could always save a world file with the intact map and reload it after every game, although that might not be a viable option in your situation.