Metallic glass composites with shape memory crystals show enhanced plasticity and work-hardening capability. We investigate the influence of various critical structural aspects such as, the density of crystalline precipitates, their distribution and size, and the structural features and intrinsic properties of the phase on the deformation behavior of metallic amorphous Cu Zr composites with B2 CuZr inclusions using molecular dynamics simulations. We find that a low density of small B2 inclusions with spacing smaller than the critical shear band length controls the formation and distribution of plastic zones in the composite and hinders the formation of critical shear bands. When the free path for shearing allows the formation of mature shear bands a high volume fraction of large B2 precipitates is necessary to stabilize the shear flow and avoid runaway instability. Additionally, we also investigate the deformation mechanism of composites with pure copper crystals for comparison, in order to understand the superior mechanical properties of metallic glass composites with shape memory crystals in more detail. The complex and competing mechanisms of deformation occurring in shape memory metallic glass composites allow this class of materials to sustain large tensile deformation, even though only a low-volume fraction of crystalline inclusions is present.