Mining subsidence disasters are common geological disasters. Accurate and effective identification of their deformation position is significant in preventing and controlling geological disasters and monitoring illegal mining. In this study, deep learning, combined with a support vector machine (SVM), has been used to establish an automatic-detection method for mining subsidence basins using Sentinel-1A data. The Huainan mining area was selected as the experimental area to verify the method. The interferogram was obtained using differential radar interferometry (D-InSAR) to process the Sentinel-1A radar data of seven landscapes, and the mining subsidence basin and other targets were extracted manually as training samples. Subsequently, AlexNet, VGG19, and ResNet50 convolutional neural networks (CNNs) were used to extract feature vectors of mining subsidence basins for the SVM classifier, and mining subsidence basins were detected in a large-area InSAR interferogram. Non-maximum suppression was used to remove the repeated search box to improve the detection accuracy of mining subsidence basins; the artificial fish swarm algorithm with strong optimization ability and good global convergence is introduced into SVM parameter optimization to construct an improved ResNet50_SVM model. The experimental results show that: (1) the three CNN_SVM methods can accurately detect dry-mining subsidence basins automatically in large regional interference maps, providing an essential scientific basis for the government to monitor illegal mining activities and prevent and control geological disasters in mining areas; (2) the accuracy of the CNN_SVM automatic-detection methods for mining subsidence basins is approximately 80%, and that of ResNet50_SVM for mining subsidence basin detection is 83.7%, superior to that of AlexNet_SVM and VGG19_SVM; (3) the accuracy of the improved ResNet50_SVM based on AFSA algorithm is 88.3%, which is better than the unimproved Resnet50_SVM model.