Cousins started four of the 25 games he played for the Ravens over the past three years. He appeared in all 16 games last season, starting one.
Stupar, who spent his first three NFL seasons in Buffalo, joined the Ravens this summer after the club lost Todd Heap to free agency. The Virginia product has 18 career receptions for 151 yards. He started five games over the past two seasons.
The Ravens also waived defensive lineman Cornell Banks, linebacker Anthony Leon, wide receivers Rodney Bradley, Justin Harper and Terrell Zachery, and offensive linemen Ryan Bartholomew and Brady Bond.