Cooperative spatial multiplexing (CSM) system has played an important role in wireless networks by offering a substantial improvement in multiplexing gain compared with its cooperative diversity counterpart. However, there is a limited number of research works that consider the performance of CSM systems. As such, in this paper, we have derived exact performance of CSM with amplify-and-forward and decode-and-forward relays in terms of outage capacity and ergodic capacity. We have shown that CSM systems yield a unity diversity order regardless of the number of antennas at the destination and the number of relays in the networks, which is the direct result of diversity and multiplexing gain trade-off. Our analytical expressions are corroborated by Monte-Carlo simulations.