Faults are a type of geological structure easily "reactivated" by underground mining, which destroys the internal movement and deformation laws of rocks and soil masses and causes anomalous surface sinking features. Therefore, studying the spatiotemporal evolution and deformation mechanism of mining subsidence in regions of fault occurrence is crucial for logical planning of the operating face and preventing and providing early warning of geological disasters. Considering the abnormal surface damage phenomenon in a town in the Hebei Province as the research background, this study used 46 Sentinel-1A radar images from January 3, 2019, to June 26, 2020, to investigate the spatiotemporal evolution of surface movement and deformation during the mining of the working face using the time-series InSAR deformation analysis method. Especially a four-threshold PS point selection method is proposed and applied to SBAS-InSAR monitoring. Compared with the monitoring data of 69 benchmarks in the same period, the MAE and RMSE between InSAR and leveling were 6.7 and 5.3 mm, respectively. This shows that the deformation of the mining area inverted by InSAR is reliable. Then, the response mechanism of surface deformation in a region of fault occurrence was analyzed based on separation space theory using a rock beam mechanical model. The results revealed that the abnormal damage area had been deformed since September, 2019, and the abnormal deformation continued to develop with the advancement of the working face. The termination position of the abnormal deformation was approximately linear and relatively spatially independent of the conventional subsidence basin. Additionally, the time-series deformation characteristics of different regions within the influence range of mining were different, and the surface subsidence curve in the direct influence area conformed to the conventional law of subsidence. Surface subsidence in the indirect influence area experienced a process of acceleration and then slowed; the deformation mechanism was different from the conventional movement law of rock strata. The surface outside the affected area exhibited a small uplift, and its active time was consistent with the fault slip instability time. Furthermore, after the fault was disturbed, the rock mass in the fault zone slipped towards the goaf, and a separation space was generated at the fault plane and transferred to the loose layer, which promoted the abnormal expansion of the movement range of overburden and severe deformation at the outcrops. Simultaneously, the footwall of the fault was slightly uplifted owing to the lever principle. Our research results provide data-driven support for the study of abnormal damage laws and the disclosure of their causes. These findings are imperative for the development and improvement of the subsequent subsidence control theory.