Cutting them off at ground level just doesn't work. I dig out any (dig deep and follow the root) that invade the flower garden from the raspberry strip. It's a big job when you first do it, then it's up to you to keep them in their own area. Blackberry branches bend and root where the tip touches ground. They were much harder to dig out for me but I did it. Keep at least 2' clear of raspberries (at the point where they want to enter your daylily garden) and they will still detect the nice, soft soil and the roots will run for it.
Someone suggested burying aluminum flashing (available at Home Depot) but the edges are sharp and I wasn't willing to risk my hands or fingers.