In this paper, we consider a cooperative underlay cognitive radio network with K half-duplex decode-and-forward relays that are used by the source-destination pairs of both the primary network (PN) and secondary network (SN). The SN exploits buffers with size of L data elements at relays to store the incoming secondary information and retransmit it later. We propose a novel buffer-aided relay selection scheme with successive interference cancellation and optimal SN power allocation that allows to mitigate the mutual interference between PN and SN. Using extensive simulations, we investigate performance of the proposed scheme in terms of the secondary throughput and power expenditure. Our results show that the proposed policy manages the interference between PN and SN efficiently, minimizes secondary power consumption and achieves higher secondary throughput compared to the recently proposed policy.