You can see a list of all routes that you've saved on your My Routes page. From here you can manage the list, including deleting any that you don't need.
To access your My Routes page, select My Routes from the Routes menu. You can also click the Manage Routes button on the My Routes tab on your personal home page.
Once on the My Routes page click the trash can icon to delete the route you don't need any more.
Once a route has been deleted it will be instantly removed from our database, so nobody else will be able to see it. This can't be undone though, so if you think you might need the route again it would be a good idea to download it first, so that you have a copy.