Accurate 3D medical image segmentation demands architectures capable of reconciling global context modeling with spatial topology preservation. While State Space Models (SSMs) like Mamba show potential for sequence modeling, existing medical SSMs suffer from encoder-decoder incompatibility: the encoder's 1D sequence flattening compromises spatial structures, while conventional decoders fail to leverage Mamba's state propagation. We present DM-SegNet, a Dual-Mamba architecture integrating directional state transitions with anatomy-aware hierarchical decoding. The core innovations include a quadri-directional spatial Mamba module employing four-directional 3D scanning to maintain anatomical spatial coherence, a gated spatial convolution layer that enhances spatially sensitive feature representation prior to state modeling, and a Mamba-driven decoding framework enabling bidirectional state synchronization across scales. Extensive evaluation on two clinically significant benchmarks demonstrates the efficacy of DM-SegNet: achieving state-of-the-art Dice Similarity Coefficient (DSC) of 85.44% on the Synapse dataset for abdominal organ segmentation and 90.22% on the BraTS2023 dataset for brain tumor segmentation.