Chiza : Yup, that's it. My arms are all scratched up from reaching through the azaleas trying to clip this wicked stuff at the root. I know that if I don't stay at it, it will quickly over-run the shrubs.
@CaffeineFree : Wear gloves; sometimes you can reach the stem near the ground and pull the whole thing out. When clipped, it usually grows back, quickly.
You can also clip it down low, and spray the stump with Roundup, being careful not to spray Azalea leaves.