We propose transmit antenna selection with receive maximal-ratio combining (TAS/MRC) as an effective approach to reduce interference in cognitive multiple-input multiple-output (MIMO) relay networks. To demonstrate this, we derive new closed-form expressions for the exact and asymptotic outage probability of TAS/MRC with multiple antennas at the primary and secondary users. We consider underlay spectrum sharing where the secondary users (SUs) transmit in the presence of multiple primary users (PUs). We consider independent Nakagami-m fading in both the primary and secondary networks. Several important design insights are revealed. We find that TAS/MRC achieves a full diversity when the transmit power at the SUs is proportional to the peak interference power at the PUs. Furthermore, we highlight that this diversity gain is completely independent of the number of antennas at the PUs.