Metallic glass composites (MGCs) containing crystals can display tensile ductility, overcoming the catastrophic failure of bulk metallic glasses. However, MGCs containing crystals with dislocation-mediated plasticity generally undergo strain-softening, but MGCs containing shape memory crystals can exhibit strain-hardening. The origin of large ductility and strain-hardening of shape memory MGCs as well as the interactions of shear bands (SBs) with crystals remains elusive. Here, two kinds of MGCs containing crystals with dislocation-mediated plasticity or shape memory crystals with martensitic transformations are investigated. It is found that the behavior and properties of SBs in glass matrix can be significantly altered by deformation characteristics of crystals. If crystals deform via dislocations, SBs are narrow, sharp and become mature. In comparison, SBs in shape memory MGCs continuously broaden without maturing by following the growth of thick martensitic plates. Broad SBs tend to bifurcate during propagation, and bifurcated SBs further induce the formation of more martensitic variants in crystals, benefiting strain delocalization. Broadening and bifurcation of SBs cause the SB blunting, which governs the superior mechanical properties of shape memory MGCs. These findings not only deepen the understanding of SBs in glass materials, but also provide a fundamental basis to enhance their mechanical properties by engineering of blunt SBs.