A new and distinct cultivar of Osteospermum plant named ‘DAOSNITTEN’, characterized by its vigorous growth, with globular upright to spreading shape well branching (4-6 per plant) habit, with stiff and strong lateral stems and thick leaves (color of leaves RHS 139A (upper side) RHS 138A (underside)) big inflorescence with strong ray florets with unique color combination (RHS N80C with stripes of N80B) at the upper side, and inflorescence that stays open, even in cold and dark weather conditions.