Gallium nitride offers an ideal material platform for next-generation high-power electronics devices, which enable a spectrum of applications. The thermal management of the ever-growing power density has become a major bottleneck in the performance, reliability, and lifetime of the devices. GaN/diamond heterostructures are usually adopted to facilitate heat dissipation, given the extraordinary thermal conduction properties of diamonds. However, thermal transport is limited by the interfacial conductance at the material interface between GaN and diamond, which is associated with significant mechanical stress at the atomic level. In this work, we investigate the effect of mechanical strain perpendicular to the GaN/diamond interface on the interfacial thermal conductance of heterostructures using full-atom non-equilibrium molecular dynamics simulations. We found that the heterostructure exhibits severe mechanical stress at the interface in the absence of loading, which is due to lattice mismatch. Upon tensile/compressive loading, the interfacial stress is more pronounced, and the strain is not identical across the interface owing to the contrasting elastic moduli of GaN and diamond. In addition, the interfacial thermal conductance can be notably enhanced and suppressed by tensile and compressive strains, respectively, leading to a 400% variation in thermal conductance. More detailed analyses reveal that the change in interfacial thermal conductance is related to the surface roughness and interfacial bonding strength, as described by a generalized relationship. Moreover, phonon analyses suggest that the unequal mechanical deformation under compressive strain in GaN and diamond induces different frequency shifts in the phonon spectra, leading to an enhancement in phonon overlapping energy, which promotes phonon transport at the interface and elevates the thermal conductance and vice versa for tensile strain. The effect of strain on interface thermal conductance was investigated at various temperatures. Based on the mechanical tunability of thermal conductance, we propose a conceptual design for a mechanical thermal switch that regulates thermal conductance with excellent sensitivity and high responsiveness. This study offers a fundamental understanding of how mechanical strain can adjust interface thermal conductance in GaN/diamond heterostructures with respect to mechanical stress, deformation, and phonon properties. These results and findings lay the theoretical foundation for designing thermal management devices in a strain environment and shed light on developing intelligent thermal devices by leveraging the interplay between mechanics and thermal transport.