How to serve static files from a different directory than the static path?

Delete static_path from the app settings.

Then set your handler like:

handlers = [
            (r'/(favicon\.ico)', tornado.web.StaticFileHandler, {'path': favicon_path_dir}),
            (r'/static/(.*)', tornado.web.StaticFileHandler, {'path': static_path_dir}),
            (r"https://stackoverflow.com/", WebHandler)
]