This is very quick and easy to do and works on both PC and Consoles: Go to the apartment, Customize Skater, then Create a new skater ( you can have up to 5 custom skaters at once. You can delete older ones and make new ones if you need to). Having a new custom skater will give you a fresh story mode.

Note: this will not reset your historical challenges.. it only gives you a new story but you keep your inventory and money