Cut stems close to ground level and immediately treat cut surface with herbicide glyphosate (Roundup or equivalent product) applied at high concentration e.g. 1 part glyphosate : 2 parts water; apply herbicide mix with spray.
The plant’s natural protective mechanism acts very quickly to seal off the cut surface which stops herbicide penetration into the sap stream. It is therefore important to treat the cut surface immediately, i.e. within 30 seconds after cut; the longer the treatment is delayed, the poorer the result will be. If necessary cut and treat each stem of a multi-stemmed plant such as Briar Rose separately to avoid a delayed herbicide treatment.