In recent years, accelerated bridge construction has led to the substantial application of precast post-tensioned segmental (PPS) bridge piers. However, PPS piers are not widely used in high-seismicity regions due to their low energy-dissipation capacity (EDC). To address this deficiency, a series of shape memory alloy (SMA)–concrete composite PPS piers were examined in this work. Non-linear static and dynamic analyses were performed on experimentally validated finite-element models of the SMA–concrete composite piers and the results were compared with those of piers without SMA bars. It was found that the length, area and post-tensioning ratio of the SMA bars affected the EDC of the piers, and an optimal design of the bars is required to reach the highest EDC possible. The effects of SMA bars on the frequency response functions of piers were investigated for the first time in this study and it was found that, unlike the piers without SMA bars, sub-harmonics and super-harmonics were not seen in the responses of the SMA–concrete composite piers, mainly the drift responses. Furthermore, the SMA–concrete composite piers experienced a significant reduction in drift responses compared with piers without SMA bars.