In this paper, the outage analysis of a wireless-powered relaying based dual-hop mixed free space optical-radio frequency (FSO-RF) system, which consists of a source (S), a relay (R), a destination (D), and a power beacon (PB), is studied. Specifically, we consider the case where S sends an optical signal to R, R processes the received signal, converts it into a RF signal, and transmits it to D with the energy harvested from PB. Assuming R is with a nonlinear energy harvester, the effects of atmospheric turbulence, two types of detection techniques, pointing error, and saturation threshold of the energy harvester on the outage performance are studied. Specifically, the analytical and asymptotic expressions for outage probability as well as the diversity order are derived. In addition, Monte Carlo simulation results are used to verify the accuracy of the derived expressions.