Mechanical deformation can potentially provide an effective means of controlling the nanoscale morphology in hybrid materials. The challenge, however, is establishing optimal couplings of the deformation and mechano-responsive components in the material to achieve nanoscopic structural reorganization without causing catastrophic damage. Through computational modeling, we investigate how torsion can be utilized to induce controllable structural changes in networks formed from binary mixtures (A and B) of polymer-grafted nanoparticles (PGNs). The nanoparticles’ rigid cores are decorated with a corona of grafted polymers, which contain reactive functional groups at the chain ends. With the overlap of the neighboring coronas, these reactive groups form labile bonds, which can reform after breakage. The labile bond energy between similar PGNs ($U\{AA}$, $U\{BB}$) is different than the energy between dissimilar species ($U\_{AB}$). By tailoring the relative values of these bond energies and the boundary conditions acting on the system, the application of a torsional deformation can result in a controllable reconfiguration of the network, leading to intertwining helical structures, or homogeneously mixed nanocomposites. In effect, our mechano-mutable system resembles a “Rubik’s cube” material, whose nanostructure, and hence global properties, can be tailored by mechanically twisting the sample.