I'm asking this question because in my mayor save file, my character's eyes are a kind that I don't like. It has been bothering me for a while, but I have recently found out that you can determine your eye type with the way you respond to Rover's questions at the beginning of the game. I would like to find out if I made a different save file with the eye type that I would like, and then delete my mayor save file, would my new villager save file become mayor?
Unfortunately, it's not possible to do delete the Mayor of a town. The only option is to re-create your town.
When Isabelle asks you "Shall we get you started?" on the main screen, the process of deleting a character is usually "I need help first..." -> "Demolish my home." If you do this on any other character except for the Mayor, that character and his/her house will be removed from the game.
However, if you attempt to do this as the Mayor, Isabelle will initially freak out, and then start to cry, explaining that the town cannot function without a Mayor. Instead, she offers the suggestion that if you really want to start over, you'll have to select "Re-create the town.", which will erase both the Mayor, the town, and all of its citizens.
This was pretty much answered by teacupgrunge in a comment which I didn't notice before but I feel it deserves a spot as an answer on the list
If you have a friend or sibling that you really trust, ask them for help then bring all of your items you've acquired and want to keep over to their world and start over. Then go back to their town and grab all of your stuff and bring it back.
If you are far along in the game, you will lose all progress in the museum and with all the shop upgrades. So for someone like me who is considering doing this but has been playing for a month now its gonna be rough but if you are only a few days into the game I think this option would work fine.
Honestly I think this is worth it for me because I don't want to have to look at my characters ugly mug all day or wear nothing but the jesters mask 24/7. But however you want to go about it is your choice.