Recently synthesized low-density cubic BC2N exhibits surprisingly high shear strength inferred by nanoindentation in stark contrast to its relatively low elastic moduli. We show by first-principles calculation that this intriguing phenomenon can be ascribed to a novel structural hardening mechanism due to the compressive stress beneath the indenter. It significantly strengthens the weak bonds connecting the shear planes, yielding a colossal enhancement in shear strength. The resulting biaxial stress state produces atomistic fracture modes qualitatively different from those under pure shear stress. These results provide the first consistent explanation for a variety of experiments on the low-density cubic BC2N phase across a large range of strain.