In this work, the molecular dynamics (MD) simulation was applied to design a laminated composite structure comprised of the shape memory alloy (SMA) and Cu-Zr metallic glasses (MGs). A wide range of MG compositions was considered to tune the mechanical features and improve the homogenous plastic deformation during the tension loading. The results indicated that the martensitic transformation in the SMA inhibited the sudden shear band propagation in the composite for all the samples. Moreover, it was revealed that the mechanism of plasticity was significantly affected by the change of MG composition. In the Cu-rich MGs, the formation and propagation of thick shear bands occurred at the end of the tension loading; however, the increase in Zr content induced the interaction of multiple shear bands with finer configurations in the system. Nevertheless, the excessive Zr addition in the MG composition facilitated the aggregation of nanopores at the interface of SMA and MGs, which may be due to the softening effect in the Zr-rich MGs. Finally, it is concluded that an optimized MG composition is required for the trade-off between the plasticity and the strength in the SMA-MG composites.