Do you mean how far back to cut the branches? You wrote roots.
And yes, the red blooms are most likely the commonly used graft
Rose (Rosa 'Dr. Huey')
Those stems (suckers) originate from below the graft and you need to preferable snap those off at the base, just cutting the branches won't do it. "Suckers are vigorous canes growing from the rootstock below the graft union on grafted roses. Cut these off to the main stem, even if you have to dig away some soil to get to them.
Pruning Roses
