It's not useless. You can leave it and make the bow as is, or thin the sapwood if you wish. I've chased a single, very thin yew ring for the back of a selfbow, so I know it can be done, but you've got to use a really light touch.
Others have thinned them without bothering to follow a single ring, violating many in the process, and then backed them with rawhide... others even let them go unbacked and never had them lift a splinter.
How many rings per inch in this stave?