Recent advances in tuning electronic, magnetic, and topological properties of two-dimensional (2D) magnets have opened a new frontier in the study of quantum physics and promised exciting possibilities for future quantum technologies. In this study, we find that the dual-gate technology can well tune the electronic and topological properties of antiferromagnetic (AFM) even septuple-layer (SL) MnBi$_2$Te$_4$ thin films. Under an out-of-plane electric field that breaks $mathcal{PT}$ symmetry, the Berry curvature of the thin film could be engineered efficiently, resulting in a huge change of anomalous Hall (AH) signal. Beyond the critical electric field, the double-SL MnBi$_2$Te$_4$ thin film becomes a Chern insulator with a high Chern number of 3. We further demonstrate that such 2D material can be used as an AFM switch via electric-field control of the AH signal. These discoveries inspire the design of low-power memory prototype for future AFM spintronic applications.