This letter proposes a dual-hop two-way full-duplex cooperative system, where spatial modulation is used at the sources and energy harvesting is employed at the wireless powered relay. We combine the physical-layer network coding and the fixed-gain amplify-and-forward relaying techniques for two-way transmission. For the simultaneous information and wireless power transfer, the power-splitting protocol is employed at the relay, which has no external power supply. A new unified tight upper-bound bit error rate (BER) expression is derived in a closed-form for both full-duplex and half-duplex transmission schemes. The accuracy of our analyses is verified by various Monte Carlo type computer simulations. The numerical results reveal that the full-duplex scheme can provide considerably better BER performance compared to the conventional half-duplex scheme as the quality of loop-interference cancellation improves and/or the spectral efficiency requirement increases.