Instructions
Turn on your Wii, select the "Mii Channel" and click "Start." This will take you to the "Mii Plaza," where you will see all of your created characters milling around.
Hover your digital hand over the character you want to delete and press the "A" and "B" buttons simultaneously. This will select and pick up the character.
Drag the character to the "Erase Mii" icon on the left side of the screen (when the Mii is set to be erased, his or her face will appear in the icon).
Let go of "A" and "B" and the Mii will be erased.