Device-to-device (D2D) communication is a key enabling technology to facilely realizing the Internet of Things (IoT) due to its spectral and energy efficiencies features. Exploiting the physical-layer network coding (PNC) and energy harvesting (EH) technology, two-way relaying (TWR) D2D communication can achieve significant performance for IoT in terms of data rate and energy efficiency (EE). In this article, we investigate the EH-aided TWR D2D communication sharing the uplink (UL) spectrum of the traditional cellular networks. We assume that the D2D transmitters, receivers, and participating relays can collect renewable energy (RE) from natural resources. Also, the relays are considered to be powered by radio-frequency (RF) signals utilizing the power splitting (PS) protocol. Subject to the Quality of Service (QoS), power, subchannel assignment, EH, and maximum practical power constraints, two nonconvex mixed-integer nonlinear programming (MINLP) problems are formulated. The two problems provide a tradeoff on either maximizing the TWR D2D link (TDL) rate or its EE depending on the IoT application needs. Based on the particle swarm optimization (PSO) algorithm, we propose the rate and EE tradeoff EH-based algorithm (REET-EH) to deal with these problems. The proposed algorithm can optimally perform the resource allocation (RA), PS factors determination, power allocation (PA), and relay selection processes. The numerical results investigate the performance of the REET-EH algorithm and show its consistency over several parameters. Also, the results illustrate that our proposed algorithm improves the system performance compared with other state-of-the-art algorithms with regard to the D2D link rate and EE.