The feature representation learning process greatly determines the performance of networks in classification tasks. By combining multiscale geometric tools and networks, better representation and learning can be achieved. However, relatively fixed geometric features and multiscale structures are always used. In this article, we propose a more flexible framework called the multiscale dynamic curvelet scattering network (MSDCCN). This data-driven dynamic network is based on multiscale geometric prior knowledge. First, multiresolution scattering and multiscale curvelet features are efficiently aggregated in different levels. Then, these features can be reused in networks flexibly and dynamically, depending on the multiscale intervention flag. The initial value of this flag is based on the complexity assessment, and it is updated according to feature sparsity statistics on the pretrained model. With the multiscale dynamic reuse structure, the feature representation learning process can be improved in the following training process. Also, multistage fine-tuning can be performed to further improve the classification accuracy. Furthermore, a novel multiscale dynamic curvelet scattering module, which is more flexible, is developed to be further embedded into other networks. Extensive experimental results show that better classification accuracies can be achieved by MSDCCN. In addition, necessary evaluation experiments have been performed, including convergence analysis, insight analysis, and adaptability analysis.