You cannot edit the face of a Mii character that was added to Manage Mii Characters from within the game.
Follow the below steps to edit a Mii character.
Note: You will need to log in on the Nintendo Account website.
1. Tap Menu, then tap the Mii icon.
2. Tap the Mii character you want to edit on the Manage Mii Characters screen.
3. Tap Remove Mii in the bottom right of the screen.
4. Tap Add a Mii, then tap Choose / Create a Mii.
5. Tap the Mii character you'd like to edit, then tap Edit.
6. Tap Select this Mii under Please Select a Mii.
7. Tap "Do you want to use this Mii with Nintendo Account?" then tap Yes.