Community discovery is a central problem in the analysis of dynamic social networks. Traditional community discovery methods mainly focus on the formation and dissolution of links between nodes, and therefore often fail to capture the richer spatial structure and temporal dependency underlying network evolution. To address this limitation, we propose STEC-Net, a spatiotemporal graph neural framework for community discovery in dynamic social networks. STEC-Net integrates spatial structure and temporal dynamics within a unified embedding architecture. First, Graph Convolutional Networks (GCNs) are used to learn snapshot-level node representations from network topology. To adapt the spatial encoder to structural evolution, a GRU-based weight evolution mechanism is introduced to update the GCN parameters over time. Then, a second Gated Recurrent Unit (GRU) is employed to model temporal dependencies across snapshot embeddings and to learn spatiotemporal node representations. Finally, a Self-Organizing Map (SOM) is applied to the learned embeddings to cluster nodes and infer their community affiliations. Experiments on four types of dynamic networks show that STEC-Net consistently outperforms traditional community discovery methods in terms of purity, normalized mutual information, homogeneity, and completeness. These results demonstrate that STEC-Net can effectively uncover evolving community structures in dynamic social networks.