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The convolutional-based methods provide good segmentation performance in the medical image segmentation task. However, those methods have the following challenges when dealing with the edges of the medical images: (1) Previous convolutional-based methods do not focus on the boundary relationship between foreground and background around the segmentation edge, which leads to the degradation of segmentation performance when the edge changes complexly. (2) The inductive bias of the convolutional layer cannot be adapted to complex edge changes and the aggregation of multiple-segmented areas, resulting in its performance improvement mostly limited to segmenting the body of segmented areas instead of the edge. To address these challenges, we propose the CM-MLP framework on MFI (Multi-scale Feature Interaction) block and ACRE (Axial Context Relation Encoder) block for accurate segmentation of the edge of medical image. In the MFI block, we propose the cascade multi-scale MLP (Cascade MLP) to process all local information from the deeper layers of the network simultaneously and utilize a cascade multi-scale mechanism to fuse discrete local information gradually. Then, the ACRE block is used to make the deep supervision focus on exploring the boundary relationship between foreground and background to modify the edge of the medical image. The segmentation accuracy (Dice) of our proposed CM-MLP framework reaches 96.96%, 96.76%, and 82.54% on three benchmark datasets: CVC-ClinicDB dataset, sub-Kvasir dataset, and our in-house dataset, respectively, which significantly outperform the state-of-the-art method. The source code and trained models will be available at https://github.com/ProgrammerHyy/CM-MLP.