Neuron segmentation is the cornerstone of reconstructing comprehensive neuronal connectomes, which is essential for deciphering the functional organization of the brain. The irregular morphology and densely intertwined structures of neurons make this task particularly challenging. Prevailing CNN-based methods often fail to resolve ambiguous boundaries due to the lack of long-range context, whereas Transformer-based methods suffer from boundary imprecision caused by the loss of voxel-level details during patch partitioning. To address these limitations, we propose NeuroMamba, a multi-perspective framework that exploits the linear complexity of Mamba to enable patch-free global modeling and synergizes this with complementary local feature modeling, thereby efficiently capturing long-range dependencies while meticulously preserving fine-grained voxel details. Specifically, we design a channel-gated Boundary Discriminative Feature Extractor (BDFE) to enhance local morphological cues. Complementing this, we introduce the Spatial Continuous Feature Extractor (SCFE), which integrates a resolution-aware scanning mechanism into the Visual Mamba architecture to adaptively model global dependencies across varying data resolutions. Finally, a cross-modulation mechanism synergistically fuses these multi-perspective features. Our method demonstrates state-of-the-art performance across four public EM datasets, validating its exceptional adaptability to both anisotropic and isotropic resolutions. The source code will be made publicly available.