Magnetic properties and spin dynamics have been studied for the structurally ordered double perovskite Sr2CoOsO6. Neutron diffraction, muon-spin relaxation, and ac-susceptibility measurements reveal two antiferromagnetic (AFM) phases on cooling from room temperature down to 2 K. In the first AFM phase, with transition temperature TN1=108 K, cobalt (3d7, S=3/2) and osmium (5d2, S=1) moments fluctuate dynamically, while their average effective moments undergo long-range order. In the second AFM phase below TN2=67 K, cobalt moments first become frozen and induce a noncollinear spin-canted AFM state, while dynamically fluctuating osmium moments are later frozen into a randomly canted state at T≈5 K. Ab initio calculations indicate that the effective exchange coupling between cobalt and osmium sites is rather weak, so that cobalt and osmium sublattices exhibit different ground states and spin dynamics, making Sr2CoOsO6 distinct from previously reported double-perovskite compounds.