Despite numerous studies on the atomic structures of Cu-Zr metallic glasses (MGs), their inherent structural ordering, e.g., medium range order (MRO), remains difficult to describe. Specifically lacking is our understanding of how the MRO responds to deformation and the associated changes in atomic mobility. In this study, we focus on the impact of deformation on MRO and associated effect on diffusion in a well-relaxed Cu 64.5 Zr 35.5 MG by molecular dynamics simulations. The Cu-Zr MG exhibits a larger elastic limit of 0.035 and a yield stress of 3.5 GPa. Cluster alignment method was employed to characterize the icosahedral short range order (ISRO) and Bergman type medium range order (BMRO) in the models upon loading and unloading. From this analysis, we find the disruption of both ISRO and BMRO occurs as the strain reaches about 0.02, well below the elastic limit. Within the elastic limit, the total fractions of ISRO or BMRO can be fully recovered upon unloading. The diffusivity increases 6-8 times in regions undergoing plastic deformation, which is due to the dramatic disruption of the ISRO and BMRO. By mapping the spatial distributions of the mobile atoms, we demonstrate the increase in atomic mobility is due to the extended regions of disrupted ISRO and more importantly BMRO.