Which "peppermint" rose are you referring to? There is the species, R. Arkansana "Peppermint" which flowers on LAST year's growth only. There are some modern roses which have Peppermint in their names and those should flower on new wood. No, not all roses flower on new growth. Many Old Garden Roses, most species and some very cold hardy newer modern roses flower mostly, or exclusively on growth that ocurred last year. If they are pruned as you would a repeat flowering type, they won't give you any flowers this year.