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Surface subsidence hazards in mining areas are common geological disasters involving issues such as vegetation degradation and ground collapse during the mining process, which also raise safety concerns. To address the accuracy issues of traditional prediction models and study methods for predicting subsidence in open-pit mining areas, this study first employed 91 scenes of Sentinel-1A ascending and descending orbits images to monitor long-term deformations of a phosphate mine in Anning City, Yunnan Province, southwestern China. It obtained annual average subsidence rates and cumulative surface deformation values for the study area. Subsequently, a two-dimensional deformation decomposition was conducted using a time-series registration interpolation method to determine the distribution of vertical and east–west deformations. Finally, three prediction models were employed: Back Propagation Neural Network (BPNN), BPNN optimized by Genetic Algorithm (GA-BP), and BPNN optimized by Artificial Bee Colony Algorithm (ABC-BP). These models were used to forecast six selected time series points. The results indicate that the BPNN model had Mean Absolute Errors (MAE) and Root Mean Squared Errors (RMSE) within 7.6 mm, while the GA-BP model errors were within 3.5 mm, and the ABC-BP model errors were within 3.7 mm. Both optimized models demonstrated significantly improved accuracy and good predictive capabilities.