If a rose is budded onto an understock, the understock can send up suckers which could, in time , take over the main rose. To get rid of suckers, dig down alongside of the rose so you can see where it is coming from, then grasp it tightly and yank downwards. What you are doing is trying to make a wound as the rose will heal it with a callous. When this happens the sucker can't come again. If you just cut it off it will be the same as pruning. Because pruning activates a rose to grow, this will just make the sucker more vigorous and could encourage more to grow.