Incorporating nanoparticles (NPs) into polymers is a practical method to tune the mechanical properties of the material. In such composite systems, it is well accepted that the interface properties at the NP surface play a vital role. In this study, by performing coarse-grained molecular dynamics simulations, we study the cavitation and strain-softening behavior of polymer/nanoparticle composites (PNCs) in a glassy state under a triaxial tensile deformation process. NPs are well dispersed in the system by a bimodal grafting of sparsely long chains and a dense layer of short diblock copolymers (sDBC) shielding the NP core. The long grafted chains and the outer block in sDBC penetrating into the matrix are chemically identical with the latter. We demonstrate that by modifying the interaction strength between the NP surface and the inner block of sDBC chains directly grafted on, cavitation process and therefore strain-softening behavior of the PNC material can be largely manipulated. In particular, we find that with a weak or repulsive interaction between NP and the inner block, the strain-softening effect can be largely suppressed and therefore the toughness can be largely enhanced. Different material properties can be attributed to different responses of the densely grafted corona structure of sDBC to the elongational tensile deformation. We hope our simulation results can be helpful for the property design of related PNC materials.