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Tailoring optical nonlinear effects (e.g. harmonic generation, sum-frequency mixing, etc.) in the recently emerging all-dielectric platform is important for both the fundamental science and industrial development of high-efficiency, ultrafast, and miniaturized photonic devices. In this work, we propose a novel paradigm for dynamically switchable high-harmonic generation in Silicon nanodimer metasurfaces by exploiting polarization-controlled dual bound states in the continuum (BIC). Owing to the high-quality factor of BIC resonances, efficient harmonic signals including the third-harmonic generation and fifth-harmonic generation from a direct process as well as a cascaded process by degenerate four-wave mixing are obtained. Moreover, the BICs and their resonantly enhanced harmonics can be switched on or off with high selectivity respect to the fundamental pump polarization. Compared with previous reports, our work provide a simple but effective tuning strategy by fully exploring the structural symmetry and polarization degree of freedom rather than resorting to additional external stimuli, which would have great advantages in smart designing tunable and switchable nonlinear light source for chip-scale applications.