RS3Mamba is a novel dual-branch network designed for remote sensing image semantic segmentation, incorporating the Visual State Space (VSS) model. The VSS model, represented by Mamba, offers efficient long-range modeling with linear computational complexity. RS3Mamba uses VSS blocks to create an auxiliary branch that provides additional global information to the main convolutional branch. A Collaborative Completion Module (CCM) is introduced to enhance and fuse features from both branches, improving cross-branch semantic fusion. Experimental results on the ISPRS Vaihingen and LoveDA Urban datasets show that RS3Mamba outperforms existing methods based on CNNs and Transformers in terms of performance metrics such as mF1 and mIoU. The method achieves significant improvements in segmentation accuracy, particularly for challenging categories like agriculture. Ablation studies confirm the effectiveness of the VSS auxiliary branch and CCM in enhancing feature extraction and representation learning. Computational complexity analysis shows that RS3Mamba has lower complexity compared to Transformer-based methods like TransUNet. The proposed RS3Mamba is the first vision Mamba specifically designed for remote sensing image semantic segmentation, offering a practical way to introduce Mamba into remote sensing tasks. The source code is available at https://github.com/sstary/SSRS.RS3Mamba is a novel dual-branch network designed for remote sensing image semantic segmentation, incorporating the Visual State Space (VSS) model. The VSS model, represented by Mamba, offers efficient long-range modeling with linear computational complexity. RS3Mamba uses VSS blocks to create an auxiliary branch that provides additional global information to the main convolutional branch. A Collaborative Completion Module (CCM) is introduced to enhance and fuse features from both branches, improving cross-branch semantic fusion. Experimental results on the ISPRS Vaihingen and LoveDA Urban datasets show that RS3Mamba outperforms existing methods based on CNNs and Transformers in terms of performance metrics such as mF1 and mIoU. The method achieves significant improvements in segmentation accuracy, particularly for challenging categories like agriculture. Ablation studies confirm the effectiveness of the VSS auxiliary branch and CCM in enhancing feature extraction and representation learning. Computational complexity analysis shows that RS3Mamba has lower complexity compared to Transformer-based methods like TransUNet. The proposed RS3Mamba is the first vision Mamba specifically designed for remote sensing image semantic segmentation, offering a practical way to introduce Mamba into remote sensing tasks. The source code is available at https://github.com/sstary/SSRS.