In this paper, we study the performance of simultaneous wireless information and power transfer (SWIPT) technique in a multi-destination dual-hop underlay cognitive relay network with multiple primary receivers. Information transmission from the secondary source to destinations is performed entirely via a decode-and-forward (DF) relay. The relay is assumed to have no embedded power source and to harvest energy from the source signal using a power splitting (PS) protocol and employing opportunistic scheduling to forward the information to the selected destination. We derive analytical expressions for the outage probability assuming Rayleigh fading channels and considering the energy harvesting efficiency at relay, the source maximum transmit power and primary receivers interference constraints. The system performance is also studied at high signal-to-noise ratio (SNR) values where approximate expressions for the outage probability are provided and analyzed in terms of diversity order and coding gain. Monte-Carlo simulations and some numerical examples are provided to validate the derived expressions and to illustrate the effect of various system parameters on the system performance. In contrast to their conventional counterparts where a multi-destination diversity is usually achieved, the results show that the multi-destination cognitive radio relay networks with the SWIPT technique achieve a constant diversity order of one.