To synthesize dynamically tunable bound states in the continuum (BIC) metasurfaces in the terahertz (THz) band, in this study, a Dirac semimetal metasurface was designed for dynamic switching between THz-band BIC and quasi-BIC. We have simulated the designed metasurface, a symmetry-protected BIC with a quality factor (Q-factor) of 147 was achieved by breaking the symmetry of the structure, the variation law of the Q-factor with the asymmetry parameter was investigated, and the physical mechanism of quasi-BIC generation was determined by analyzing the surface electric field and surface current. Notably, the dynamic transition from BIC to quasi-BIC was achieved by varying the Fermi level of the Dirac semi-metal, with the maximum transmission difference of 0.61 and an almost constant resonant frequency for Fermi levels ranging from 2-20 meV. In addition, we fabricated and demonstrated a dynamic near-field display array, wherein different content is dynamically displayed by successively applying different gate voltages. This paper presents a novel design concept for dynamic switching between BIC and quasi-BIC on a metasurface and promotes the practical application of BIC metasurfaces.