Medical image segmentation holds immense potential in disease diagnosis and treatment outcome evaluation, helping doctors achieve precise lesion delineation and make informed medical decisions. However, challenges such as low signal-to-noise ratios, blurred edges, and complex structures in medical images hinder the performance of existing segmentation methods in capturing detailed texture and global semantic information. To address these issues, we propose a Wavelet-Based Global-to-Local Network for Medical Image Segmentation, named CM-YNet. Specifically, We design a wavelet transform to preprocess raw medical images, extracting high-frequency images that capture detailed texture information and low-frequency images that represent global semantic information. These processed images are fed into a Global-to-Local Network built upon Convolutional Neural Networks (CNNs) and State Space Models (SSMs), enabling the extraction of local details and modeling of global contextual information. Additionally, we introduce a Multi-Scale Adaptive Enhancement Module (MAEM) that enhances the network’s ability to integrate global-to-local features through channel fusion, multi-scale enhancement, and a convolutional block attention module. Extensive experiments on the ISIC 2017, ISIC 2018 and CVC-ClinicDB datasets demonstrate that our method achieves superior performance in medical image segmentation, as evidenced by quantitative metrics and visualized results.