Deep learning methods have become the mainstream technology for classifying and extracting urban and rural road networks based on remote sensing image data. However, the existing methods suffer from issues such as mixed occlusion of neighboring objects (such as vegetation and buildings), long model training time, and high computational complexity, and most of them only focus on independent targets such as road surface, edge line, and center line, resulting in low accuracy of road classification extraction results. In order to fully utilize the constrains of the spatial topological relationship features between road edges and road surfaces, this paper proposes a road surface extraction network, CAS-DeepNet, based on the road topological correlation feature information. Firstly, based on the DeepLabV3+network architecture, the lightweight MobileNetV2 feature extraction network is improved, and the edge enhancement module based on residual connection is embedded to capture road edge information. Secondly, a CS-ASPP structure based on dense connections is designed to improve the model performance. Then, the channel attention mechanism is introduced to effectively fuse multiple branch channels in the image to improve the feature representation ability. Finally, the road connectivity constraints are constructed through the topological association information of road edges to enhance the integrity of the road network extraction results. The experimental results on datasets, such as CHN6-CUG and DeepGlobe, show that the CAS-DeepNet designed in this paper has more advantages over popular methods, such as U-Net++, DeepLabV3+, D-LinkNet, RoadNet, ACNet, and SDUNet, in terms of accuracy rate, recall rate, F1 score, and overall accuracy rate, significantly improving the accuracy and completeness of the extraction results of road network. This road surface fine extraction method based on road topology correlation features proposed in this study can provide basic support for natural resource survey and monitoring, as well as geospatial environment perception modeling.