This paper analyzes the effects of realistic relay transceiver on the outage probability and throughput of a two-way relay cognitive network that is equipped with an energy-harvesting relay. In this paper, we configure the network with two wireless power transfer policies and two bidirectional relaying protocols. Furthermore, the differences in receiver structure of relay node that can be time switching or power splitting structure are also considered to develop closed-form expressions of outage and throughput of the network providing that the delay of transmission is limited. Numerical results are presented to corroborate our analysis for all considered network configurations. This paper facilitates us not only to quantify the degradation of outage probability and throughput due to the impairments of realistic transceiver but also to provide an insight into practical effects of specified configuration of power transfer policy, relaying protocol, and receiver structure on outage and throughput. For instance, the system with multiple access broadcast protocol and the power splitting-based receiver architecture achieves ceiling throughout higher than that of the transmission rate of source nodes. On the contrary, a combination of dual-source energy transfer policy and the time division broadcast protocol is contributed the highest level of limiting factor in terms of transceiver hardware impairments on the network throughput.