It's a very old phrase that has stuck around because it still sounds a bit crass to religious people. The word "sake" is used to mean that you are doing something for someone else. If I carry your luggage for you, I'm doing it for your sake. It's an old way of saying it, but it's still used a little bit here and there. In this case, the phrase you mention is basically appealing to the other person's belief in God by saying, "If you won't stop for me, then stop for God!" It's supposed to make your feelings sound stronger because you're asking the person to stop for God's sake since they won't stop for your sake. In modern language people really only still use it because religious people hate it, so it feels like swearing.