How do I replay levels?

Every mission/level has a leaderboard score, but I can't find an obvious way to replay levels to attempt a higher ranking, even from the score menu in Settings. How can I replay specific story levels? Do I have to make a new game and play through again?

Solution 1:

The Steam version of Jet Set Radio was updated on May 24th, 2013 to add a Retry option after completing a stage.

This option is only available on the results screen shown directly after completing a stage.

If you are playing on Dreamcast or if you have already returned to the garage, your only option is to reload an old save or play through the story again. (See wolf's answer)