What you describe is very unusual. I never heard that ants eat rose shoots. It is probably a mixed problem. Usually the ants take care of the plant louses which are on the rose. So if you take care of the louses the ants should leave too. But make sure that you use an environment friendly remedy (e.g. a special oil drugs). Otherwise you could poison garden birds as well.
The other problem, the nipping off of the shoots, could be caused by the Blennocampa elongatula. The larvae are in the tip of the shoot and eat up the inside of the rose stipe. As a consequence, the shoot nips off. If my guess is right, you should see the eaten-away galleries and the larvae when you open up a shoot. Cut back the roses to the healthy tissue and throw the infected shoots into the garbage and not onto the compost heave if you really want to get rid of these pests.