Do they strap a baby down for circumcision?

Yes, usually: Known as a papoose board, this device is padded and gently holds an infant still while the delicate procedure is performed. While some might consider this device offensive, i would argue its use to be beneficial and more humane than risking allowing a child to squirm and wiggle at just the wrong moment. Babies are "carefully secured" rather than " strapped down.".