Accurate segmentation of the pancreas and its lesions in CT scans is crucial for the precise diagnosis and treatment of pancreatic cancer. However, it remains a highly challenging task due to several factors such as low tissue contrast with surrounding organs, blurry anatomical boundaries, irregular organ shapes, and the small size of lesions. To tackle these issues, we propose DB-MSMUNet (Dual-Branch Multi-scale Mamba UNet), a novel encoder-decoder architecture designed specifically for robust pancreatic segmentation. The encoder is constructed using a Multi-scale Mamba Module (MSMM), which combines deformable convolutions and multi-scale state space modeling to enhance both global context modeling and local deformation adaptation. The network employs a dual-decoder design: the edge decoder introduces an Edge Enhancement Path (EEP) to explicitly capture boundary cues and refine fuzzy contours, while the area decoder incorporates a Multi-layer Decoder (MLD) to preserve fine-grained details and accurately reconstruct small lesions by leveraging multi-scale deep semantic features. Furthermore, Auxiliary Deep Supervision (ADS) heads are added at multiple scales to both decoders, providing more accurate gradient feedback and further enhancing the discriminative capability of multi-scale features. We conduct extensive experiments on three datasets: the NIH Pancreas dataset, the MSD dataset, and a clinical pancreatic tumor dataset provided by collaborating hospitals. DB-MSMUNet achieves Dice Similarity Coefficients of 89.47%, 87.59%, and 89.02%, respectively, outperforming most existing state-of-the-art methods in terms of segmentation accuracy, edge preservation, and robustness across different datasets. These results demonstrate the effectiveness and generalizability of the proposed method for real-world pancreatic CT segmentation tasks.