In the Moving Meditation that the Astanga practice offers, and eventually truly becomes for practitioners, I find it not to be so much a "stopping" of my mind and my thoughts, but an allowance of gaining more clarity. The true, worthwhile thoughts come through and are even offered some dedicated time for contemplation and reflection.
What seems to occur during practice is that, while the running monkey mind chatter fades into the background, any clear and true thread of dialogue remains. The breath and the movement work to shake things up and sift things through and settle into place a sense of knowing. In short...things get worked out in my head!