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Mitosis nuclei count is one of the important indicators for the pathological diagnosis of breast cancer. The manual annotation needs experienced pathologists, which is very time-consuming and inefficient. With the development of deep learning methods, some models with good performance have emerged, but the generalization ability should be further strengthened. In this paper, we propose a two-stage mitosis segmentation and classification method, named SCMitosis. Firstly, the segmentation performance with a high recall rate is achieved by the proposed depthwise separable convolution residual block and channel-spatial attention gate. Then, a classification network is cascaded to further improve the detection performance of mitosis nuclei. The proposed model is verified on the ICPR 2012 dataset, and the highest F-score value of 0.8687 is obtained compared with the current state-of-the-art algorithms. In addition, the model also achieves good performance on GZMH dataset, which is prepared by our group and will be firstly released with the publication of this paper. The code will be available at: https://github.com/antifen/mitosis-nuclei-segmentation.