Light propagation and acoustic vibrations can be controlled by designing the bandgap of phoxonic crystals, which support photonic and phononic bandgaps simultaneously. In this study, we numerically investigated the optical and mechanical properties of a clover-shaped 6H-SIC crystal microcavity. The results indicate that the frequency range of the phononic bandgap can be manipulated by adjusting the geometry of the structure, resulting in a wide phononic bandgap over 12 GHz centered at 30.8 GHz. The structure also supports strong localized optical modes for visible light with a Q-factor over 143. Within the photonic and phononic bandgaps of the phoxonic crystal, the structure can reduce mechanical vibrations and support a confined optical mode that can be used for trapping nanoparticles.