How soon should I get a tetanus shot after a deep cut?

As soon as possible. Do not put this off if it has been 10 years or more since your last shot or if you don't know when it was. Get it now.
DependsImmuneStatus. It depends when you had your last Tetanus Booster.A deep cut needs Tetanus prevention only if your last booster shot was more than 5 years ago.Or you don't know when you had your last booster shot. Even though most who live in USA have been immunized with Primary Immunisation as children(with few exceptions)In last 34 years since you were born.As Adults many do not get the boosters.Ask your Doctor.