Skin lesion segmentation plays a vital role in skin diagnosis. However, the precise segmentation of skin lesion areas is difficult due to ambiguous lesion boundaries and varying lesion sizes. To address these challenges, we propose an Edge-Enhanced and Multi-scale model based on Mamba (EMM-UNet). The model employs a three-branch encoder-decoder called EM-VSS to extract edge, local, and global information, thereby enabling rich and differentiated feature capture. With the challenge of ambiguous lesion boundaries, we propose an edge enhanced convolution (EEC) module and a wavelet transform-based high-frequency enhancement (HE) module to enhance the model recognition of edges. Meanwhile, to address the challenge of varying lesion sizes, we propose a multi-scale feature extraction (MFE) module. This module extracts features from different scales, enhancing model adaptability to variations in lesion size. We perform comparative experiments on three publicly available skin lesion datasets, and the results show that EMM-UNet is highly competitive in skin lesion segmentation.