It's called Season. Those run for a few months and are then "reset". Each Season you start completely from scratch. New character, no stash, no gold, etc.
Outside Season, the only option I can think of is to switch from softcore to hardcore. Characters in Hardcore will share a stash and gold, but it will not be shared between softcore/hardcore.
So to summarize:
Each season offers a start from scratch (though only once per season again)
Switching to hardcore offers a start from scratch (only once for a lifetime)
A season offers a fresh start for softcore as well as hardcore -> 2 fresh starts per season
The next season (season 16) starts on the 18th January 2019