The study on damage and fracture of superconducting Nb₃Sn under cyclic loading is an indispensable part of understanding the origin of the irreversible strain limit in Nb₃Sn. This paper uses molecular dynamics simulation to investigate the fracture and deformation damage behavior of polycrystalline and single crystal Nb₃Sn/Nb composite materials under cyclic loading at extremely low temperatures. The effects of strain rate on crack initiation and growth were carefully analyzed in both polycrystalline and single crystal Nb₃Sn/Nb composite materials. The results indicate that slip occurs in single crystal Nb₃Sn/Nb composite materials after cyclic loading. When the local stress at the slip band intersection exceeds the material strength, microcracks initiate at the slip band intersection, leading to fracture failure of the composite material. In contrast, the failure of polycrystalline Nb₃Sn/Nb composite materials is due to the inability of stress at grain boundaries to relax under cyclic loading, which leads to the initiation of microcracks at the grain boundaries and intergranular fracture of the composite material. The analysis of the different damage, fracture, and failure mechanisms of polycrystalline and single crystal Nb₃Sn/Nb composite materials at different strain rates shows that the fracture is brittle at low strain rates. As the strain rate rises, the number of slip bands in the single crystal Nb₃Sn layer increases, enhancing the toughness of the single crystal Nb₃Sn/Nb composite material. Conversely, the influence of grain boundaries on material strength decreases in polycrystalline materials as the strain rate increases. Moreover, polycrystalline Nb₃Sn/Nb composite materials exhibit significant residual strength after local fracture of Nb₃Sn at high strain rates. The research results will contribute to a better understanding of the damage evolution process of Nb₃Sn/Nb composite materials under cyclic loading and offer theoretical guidance for optimizing material performance.