This paper outlines the scientific goals and observational strategies of the Mini-SiTian Array. Mounted at Xinglong Observatory, the Mini-SiTian Array consists of three 30 cm telescopes and has been in operation since 2022. The large field of view, combined with the capability for multi-band photometric observations, enables the Mini-SiTian Array to perform rapid follow-up observations to identify optical counterparts of gravitational waves, capture the early light curves of tidal disruption events and supernovae, and monitor stellar flares, Be star outbursts, and cataclysmic variable stars, although its limiting magnitude is not very deep. By collaborating with the Xinglong 2.16 m telescope and leveraging a real-time image processing pipeline, simultaneous photometric and spectroscopic observations could be performed to reveal their underlying physical mechanisms. The observational and research experience provides critical guidance for the implementation of the full-scale SiTian project in the future.