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Despite achieving remarkable performance, Federated Learning (FL) suffers from two critical challenges, i.e., limited computational resources and low training efficiency. In this paper, we propose a novel FL framework, i.e., FedDUAP, with two original contributions, to exploit the insensitive data on the server and the decentralized data in edge devices to further improve the training efficiency. First, a dynamic server update algorithm is designed to exploit the insensitive data on the server, in order to dynamically determine the optimal steps of the server update for improving the convergence and accuracy of the global model. Second, a layer-adaptive model pruning method is developed to perform unique pruning operations adapted to the different dimensions and importance of multiple layers, to achieve a good balance between efficiency and effectiveness. By integrating the two original techniques together, our proposed FL model, FedDUAP, significantly outperforms baseline approaches in terms of accuracy (up to 4.8% higher), efficiency (up to 2.8 times faster), and computational cost (up to 61.9% smaller).