In this paper, for a two-way relay channel comprising two multi-antenna transceivers and L single-antenna potential relay nodes, we propose three network-coded cooperative spatial multiplexing (CSM) schemes that effectively overcome the rate loss incurred due to the half-duplex limitation of the transceivers and the relay nodes and achieve high spectral efficiency. In the following, these three schemes are referred to as time-division broadcast (TDBC)-CSM, incremental (I)-TDBC-CSM and multiple-access broadcast (MABC)-CSM. We investigate these schemes in terms of the outage probability, the average transmission rate, the asymptotic behavior, and the diversity-multiplexing tradeoff. The analysis of the paper shows that, first, the I-TDBC-CSM scheme achieves the full diversity of order L min(M1, M2) + M1M2, where M1 and M2 are the numbers of antennas employed by the two transceivers; second, the TDBC-CSM and MABC-CSM schemes achieve the diversity of order L min(M1, M2),where this quantity is the maximum achievable diversity gain in the absence of the direct link between the transceivers; third, the TDBC-CSM and I-TDBC-CSM schemes effectively overcome the rate loss incurred due to the half-duplex limitation of the relay nodes; fourth, the MABC-CSM scheme not only overcomes the half-duplex limitation of the relay nodes but also mitigates the spectral efficiency loss incurred due to the half-duplex limitation of the transceivers; and fifth, if one or both of the transceivers are equipped with a massive antenna array, the asymptotic average rate of the CSM-based schemes scales linearly with the number of potential relay nodes, as opposed to the conventional relaying schemes, in which the average rate is not scalable with L. We provide extensive simulation results to confirm the theoretical analysis of the paper. The simulation results show that for a given outage probability, the proposed schemes outperform the conventional relaying schemes in terms of the average transmis...