How long does daypro (oxaprozin) take to get completely out of your system?

Couple of Days. But you may have consequences like high blood pressure, GI damage or bleeding tendencies that last far longer.
Half life. 4 half lives is usually thought to be enough time for a drug to be "gone". The half life of Daypro (oxaprozin) is 22 hours....So nearly 4 days.