Piping systems are important nonstructural components of most types of buildings. Damage to piping systems can lead to significant economic losses, casualties, and interruption of function. A survey of earthquake disaster sites shows that suspended piping systems are flexible and thus prone to large deformation, which can lead to serious damage of the piping systems. The single-sided pounding tuned mass damper (PTMD), which is an emerging vibration suppression tool, has the potential to serve as a cost effective and non-invasive solution for the mitigation of vibration in suspended piping systems. The operating frequency of the single-sided PTMD can be tuned similarly to a tuned mass damper (TMD). The single-side PTMD also possesses high energy dissipation characteristics and has demonstrated outstanding performance in vibration control. One of the key factors affecting the performance of the PTMD is the damping material, and there is a constant search for the ideal type of material that can increase the performance of the PTMD. This paper explores the use of shape memory alloy (SMA) sponge as the damping material for two types (spring steel and pendulum types) of PTMDs to mitigate the vibration of a suspended piping system. The PTMDs are tested both in free vibration and in forced vibration. The results are compared with no control, with a TMD control, and with a viscoelastic (VE) material PTMD control. The results show that in free vibration tests, SMA–PTMDs attenuate the displacement of the piping system significantly. The time to mitigate vibration (i.e., reduce 90% of the vibration amplitude) is reduced to 6% (for spring steel type) and 11% (for pendulum type) of the time taken to mitigate vibration without control. In forced vibration tests, the overall magnitudes of the frequency response are also lowered to 38% (spring steel) and 44% (pendulum) compared to vibration without control. The results indicate that SMA has the potential to be a promising energy dissipating material for PTMDs.