Yes, remove the blackened cane, there is no growth on it.
And where do you live? You didn't add that to your profile, you can edit it (click on the person icon upper right) so it appears in the upper right of your posts, see examples in our posts. The graft (that bulge at the bottom is where the rose is grafted onto a hardier rose bush rootstock) seems high and if you are in a colder zone, it would need to be planted much deeper.