Hey there,
I too use rough concrete since I live near a concrete plant. I know the problem well. Here are some thoughts:
1 If you are new to slinging, your release may be a bit off which will cause tangling of the stone in the cord. I usually was releasing too early when I had that problem. I have had the retention cord ripped off my finer when heavy stones got tangled up.
2 Your motion has to be smooth. Usually if I was trying to throw too fast, it caused tangling; probably due to the "jerking and slack in the cords.
3 Also, I find that on occation, if I sling a long stone with sharp edges they seem to get hung up in the pouch from time to time.
Even with proper technique, rough projectiles will cut away at 4-6 inches of the release cord coming from the pouch; therefore, I put duct tape tightly wrapped around the cord in this area and replace it from time to time. Or you can use whipping in this area but it is stiffer than tape.
Hope that helps