Federated Learning (FL) faces significant challenges arising from both data and system heterogeneity. While Clustered Federated Learning (CFL) mitigates data heterogeneity by grouping clients with similar data distributions, it remains vulnerable to system heterogeneity, which can slow convergence due to performance disparities among clients. Moreover, data drift may degrade clustering accuracy and training efficiency over time. In this work, we propose a Model Structure-aware Clustered Federated Learning (MSCFL) framework that simultaneously addresses the issues of data heterogeneity, system heterogeneity, and data drift. MSCFL incorporates model pruning (MP) into the CFL framework to enhance training efficiency under system heterogeneity. To enable this integration, we address the key challenge of performing effective clustering based on heterogeneous, pruned local models with varying structures. To this end, we design a model structure-based similarity computation algorithm to integrate CFL with MP. To effectively address data drift, we propose a dynamic cluster migration strategy that efficiently monitors model structures via Hamming Distance and triggers re-clustering only when necessary. Extensive experimental results show that MSCFL improves the accuracy and convergence speed of cluster models, outperforming traditional CFL in various settings. Additional results and our codes are available in supplementary materials.