In this paper, we analyze the secrecy performance of a two-hop cooperative network consisting solely of energy-harvesting self-sustaining nodes drawing energy from a multi-antenna power beacon (PB). Performance of such networks is quite different from that with powered nodes. We consider optimal combining of the direct and relayed signals at the multi-antenna destination as well as the multi-antenna eavesdropper. Since availability of channel state information at the source is impractical in such networks, we assume fixed-rate signaling. To implement incremental signaling, we utilize feedback bits from the destination. Assuming practical nonlinear EH, exact and approximate expressions are derived for the secrecy outage probability of the selective decode-and-forward (SDF) and the incremental decode-and-forward (IDF) relaying schemes. It is demonstrated that IDF has much better secrecy performance than SDF just as with powered nodes. However, unlike with powered nodes, the secrecy performance is a convex function of the transmit power of PB. We propose a novel power back-off scheme to improve secrecy under different network operating conditions. The security-reliability trade-off (SRT) is analyzed to highlight the trade-off between outage and secrecy performance with the power back-off scheme. Simulation results validate the analytical expressions.