Usually, you will have to beat the game to start a new run, but there is a way around that. All you have to do is follow these easy steps (note: you have to have the game window closed for this to work):

1. Go to %appdata%/../Local/
2. Find the folder that is named "You_Have_10_Secondsfinal"
3. Delete the folder
4. Restart YH10S and you will find that you are back at area 1 without anything unlocked

Hope you found this useful, happy running!