During inspiration, the diaphragm moves downwards (and the abdominal wall moves outwards). As the airway is obstructed, the thorax cannot draw gases in, so cannot expand.
As the diaphragm continues to descend, a sub-atmospheric pressure develops in the thorax and the chest wall is drawn in (despite the intercostal muscles trying to expand the chest).
To the observer there is abdominal expansion with chest collapse. During expiration the reverse is seen. As inspiratory effort increases and expiration becomes active, the effect increases.
The severity of see-saw respiration is indicative of the severity of the airway obstruction.