This paper investigates the system outage performance of a simultaneous wireless information and power transfer (SWIPT) based two-way decode-and-forward (DF) relay network, where potential hardware impairments (HIs) in all transceivers are considered. After harvesting energy and decoding messages simultaneously via a power splitting scheme, the energy-limited relay node forwards the decoded information to both terminals. Each terminal combines the signals from the direct and relaying links via selection combining. We derive the system outage probability under independent but non-identically distributed Nakagami-m fading channels. It reveals an overall system ceiling (OSC) effect, i.e., the system falls in outage if the target rate exceeds an OSC threshold that is determined by the levels of HIs. Furthermore, we derive the diversity gain of the considered network. The result reveals that when the transmission rate is below the OSC threshold, the achieved diversity gain equals the sum of the shape parameter of the direct link and the smaller shape parameter of the terminal-to-relay links; otherwise, the diversity gain is zero. This is different from the amplify-and-forward (AF) strategy, under which the relaying links have no contribution to the diversity gain. Simulation results validate the analytical results and reveal that compared with the AF strategy, the SWIPT based two-way relaying links under the DF strategy are more robust to HIs and achieve a lower system outage probability.