Shape memory alloys (SMAs) are a class of functional materials that possess unique thermomechanical properties, such as shape memory effect (SME), superelasticity (SE), damping, and good fatigue and corrosion resistance, which enable them to become ideal materials for applications in earthquake engineering. Numerous studies have shown that the mechanical properties of superelastic SMAs mainly depend on the wire form, or the relationship between the microstructure and thermally induced phase transitions. However, extremely few studies have elucidated the effects of the heat-treatment strategy, size effect of large diameters, and cyclic loading. Herein, the mechanical properties of SMA bars, such as residual strain, energy dissipation, and equivalent damping ratio, were studied with different heat-treatment strategies, cyclic loadings, and strain amplitudes; this was achieved by conducting cyclic tensile tests on SMA bars with four different diameters. The results indicate that the maximum phase transformation stress was obtained with a 14 mm SMA bar subjected to heat treatment at 400 ℃ for 15 min. The mechanical properties were relatively stable after five loading–unloading cycles, which should be considered in engineering applications. The test results provide a mechanical basis for using large SMA bars in self-centering structures in seismic regions.