"Ideally you should have done the following as soon as you became aware of the problem, but it is not too late now: cut the suckers down to about a foot and scrape away the soil from around the rose's roots to identify the point from which it or they sprouted. Then rip them off the root in a downwards direction.

By ripping rather than cutting you will be destroying any other dormant buds close by, and the problem is far less likely to recur. Re-cover the root with soil, cover your tracks, then feed and apply a comforting mulch around the base of the rose."

The quote is from the link below.

Here is a link that might be useful: link for above