Probably you don't need poison,Lola; that would be risky for the new rose,methinks. Besides, poisons should be avoided.
When I get a stubborn rootstock or some such, I've had success just by tearing out or cutting out as much as possible, then mulching it over with a thick layer of cardboard topped by organic matter. Once in a while, I check under the cardboard, and if the sucker is still trying to grow I pull it out again, and re-cover the area. Eventually it dies off.
