The columnar-grained (CG) Cu–Al–Mn shape memory alloy samples possess a strong <001>-oriented texture along the solidification direction (SD) and straight low-energy grain boundaries fabricated by unidirectional solidification technique. When the angle between tensile direction and the SD ranged from 0° to 90° at the tensile tests, the superelasticity of samples changed in a “V” shape and showed a large anisotropy. Meanwhile, the martensite transformation critical stress of the CG Cu–Al–Mn samples increased from 258.5MPa for 0° to 521.9MPa for 45°, and then decreased to 324.3MPa. The large anisotropy of the superelasticity was attributed to the combined effects of grain orientation and grain boundaries, wherein the influence of the grain boundaries had an obvious dependence on orientation. The potential applications of CG Cu–Al–Mn alloys as anisotropic shock isolators and dampers in high rise buildings and precision instruments were also proposed.