Introducing the unique advantage of additive manufacturing technology into copper-based shape memory alloys (SMAs) to fabricate high-performance alloys has garnered great attention in recent years, but the intrinsic relationships between microstructure and mechanical properties need to be further clarified. In this paper, the microstructural evolution of ternary CuAlNi SMAs fabricated by laser powder bed fusion (LPBF) under the tensile-compressive loading was investigated to determine the underlying mechanism of tension-compression asymmetry, that is, excellent compressive but poor tensile properties. Multiscale characterization of the different deformation stages revealed the numerous activated deformation mechanism on the 18R martensite matrix. A twin-related transformation dominated the main plastic deformation process due to lower stacking faults energy and high-density pre-existing planer defects in the CuAlNi SMAs. Deformation twinning nucleated at prior austenite boundaries and developed into parallel and network structures inside the parent grain of different sizes. In addition, the preferred orientation in different stages, the stress-induced γ phase transformation, and the interaction between dislocations and stacking faults are discussed. These results not only provide significant insights to understand the detwinning and deformation twinning process of SMAs but also establish the essential framework of microstructure and mechanical properties of Cu-based SMAs fabricated by LPBF.