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Based on the time-dependent density functional theory, we theoretically investigate the influence of mechanical strains on the high-order harmonic generation (HHG) in the monolayer hexagonal boron nitride (hBN) crystal. We show that mechanical strains can largely modify the band structure and facilitate the harmonic emission. Compared to uniaxial strains, we find that biaxial strains may enhance the HHG yield significantly, and the HHG spectroscopy generated by a linearly polarized laser is closely related to the symmetry of the deformed hBN. Moreover, when driven by a circularly polarized laser, we find that the appearance of the 3n-order harmonics manifests the restoration of the three-fold rotational symmetry. Our results will be useful in controlling the HHG spectroscopy and probing lattice deformations in crystals.