What is a sucker?
Don’t mistake this problem child with a basal break. A basal break is new growth coming from the bud graft. It is sometimes reddish, depending on the variety of the rose, it is soft and succulent with no thorns. It is to be prized, as this is the next generation of blooms for your rose bush. A sucker, on the other hand, is growth coming from beneath the bud graft or bud union, that knob above the root structure of a grafted rose. The reason for it is that one or more of the buds on the rootstock was not cut completely out, so this bud keeps wanting to send out its own growth, often with 5- or 7-leaflet leaf clusters. You need to dig down in the soil and cut this growth off as close to the roots as possible, as it will just take strength from the grafted rose. It also may grow each season if not cut completely out.