I have nothing whatsoever against sedums in general, in fact I have a variety of them myself.
Sedum acre specifically however (and that photo looks rather a lot like it, to me), is a PLAGUE. Because its leaves are so eensy tiny and so brittle, and each broken-off rolled-downhill washed-by-rain blown-by-wind piece will take root and because of being tiny you won't see 'em til they're well established. They can become a real problem, both in dryish or poorish natural areas and in a person's yard and garden.
That doesn't stop some people from planting this species on purpose, and sometimes it does stay contained, but, I wouldn't bet on it.
I'm with those who suspect your problem isn't so much sedums competing with roses as indicating conditions that are poor for the rose.
If it were me I'd be highly inclined to dig the rose up, deeply and widely amend the planting hole, and put it back in. Or just get a new rose, frankly (with the same heavy amendments to planting hole)
Have fun,
Pat