Accurate segmentation of polyps in the colorectal region is crucial for medical diagnosis and the localization of polyp areas. However, challenges arise from blurred boundaries due to the similarity between polyp edges and surrounding tissues, variable polyp morphology, and speckle noise. To address these challenges, we propose a Hybrid Multi-Frequency Perception Gated Selection Network (Polyp-Mamba) for precise polyp segmentation. First, we design a dual multi-frequency fusion encoder that employs Mamba and ResNet to quickly and effectively learn global and local features in polyp images. Specifically, we incorporate a novel Hybrid Multi-Frequency Fusion Module (HMFM) within the encoder, using discrete cosine transform to analyze features from multiple spectral perspectives. This approach mitigates the issue of blurred polyp boundaries caused by their similarity to surrounding tissues, effectively integrating local and global features. Additionally, we construct a Gated Selection Decoder to suppress irrelevant feature regions in the encoder and introduce deep supervision to guide decoder features to align closely with the labels. We conduct extensive experiments using five commonly used polyp test datasets. Comparisons with 14 state-of-the-art segmentation methods demonstrate that our approach surpasses traditional methods in sensitivity to different polyp images, robustness to variations in polyp size and shape, speckle noise, and distribution similarity between surrounding tissues and polyps. Overall, our method achieves superior mDice scores on five polyp test datasets compared to state-of-the-art methods, indicating better performance in polyp segmentation.