Patients with type 2 diabetes (T2D) face an increased risk of cardiovascular complications, highlighting the need for improved diagnostic methods. Epicardial adipose tissue (EAT) is recognized as an important biomarker for cardiovascular diseases (CVDs). Dixon MRI is widely used to depict adipose tissue by deriving fat and water signals, providing complementary information through multi-modality images: in-phase, out-of-phase, fat phase and water phase. This study introduces EAT-Mamba, a novel multi-modal deep learning-based approach for automated segmentation and quantification of EAT from Dixon MRI. The model architecture integrates a U-shape structure with a multi-modal fusion layer and Res-Mamba blocks to capture features across various modalities and scales. The Res-Mamba block is designed with a Mamba block, based on state space sequence models (SSMs) for long-range context learning, and a convolutional neural network (CNN)-based residual block for local feature extraction. Comprehensive evaluations were conducted on a Dixon MRI dataset involving 90 subjects, comparing EAT-Mamba against Res-UNet and UNet + + across different modality combinations. EAT-Mamba achieved a Dice similarity coefficient of 0.873, a Hausdorff distance 95 of 3.34 mm, and an average symmetric surface distance of 0.591 mm with four modalities, consistently outperforming the other methods. Notably, the use of out-of-phase and fat phase modalities can enhance EAT segmentation performance. This study provides valuable insights into the use of SSMs and multi-modal images in EAT segmentation, paving the way toward improved cardiovascular risk assessment and treatment planning in clinical practice.