you can change your mii on Mario kart without losing any data.

like if you were playing the game with your mii and wanted to race with a different one like link or Zelda.

but if you wanted to copy the save to another spot and use your mii and another for the same one I'm not sure.

edit
you can also change your mii's wight class to. you can be light,middle or heavy .
change the size of your mii to be taller or more round.