The built-in auto-save feature gives you the ability to automatically save your progress after doing various things in the game.
You can also save manually if you want to make sure your game saves where you want it to.
It is in the inn or in the world of Miitopia, click on X then and look for the option to save and exit, you can do this same step when you are in the world.
During missions the pause menu is available, and you do not have the option to save. So be sure to do it before or after any mission. We hope that after this article on how to save your game in Miitopia is presented, you can manage to save all your progress in the game.