When a baby is getting circumcised do the doctors strap the baby to a board so he can't move?

Yes for few moments. We don't want him to kick during the procedure. This neiither cruel nor torture if anesthetic cream is applied to the penis for 15 - 30 minutes beforehand. We also give the baby sweetease (sugar water) to suck down during the procedure.
Restraint board. The typical circumcision restraint is a hard plastic shell with indentation of a baby silhouette & cutouts where velcro straps can be inserted to keep the infant in position for the procedure. Infants are generally placed on the board on a blanket with a diaper. Straps assure the arms/legs do not move for the 10-15 min procedure. After initial crying most settle & some sleep during the procedure.