To my knowledge, it is not possible to reset your progress and start anew on Xbox One.
If it is merely to experience the game again, you could just create a new, free (Xbox Live Silver) account and play. If I recall correctly, Gems of War does not require that you have an Xbox Live Gold membership, so you can have at it after you go through the steps to setup a new account and gamertag.
If you just have to experience the game again on your current gamertag/profile, then you may have to contact GoW tech support. (I believe you can find it pinned at the top of the GoW Twiiter page, or somewhere here on the forums.)
Not sure how they would, but they probably could delete/reset all your progress on you current profile.