Large Language Models (LLMs) have achieved remarkable performance across tasks but remain energy-intensive due to dense matrix operations. Spiking neural networks (SNNs) improve energy efficiency by replacing dense matrix multiplications with sparse accumulations. Their sparse spike activity enables efficient LLMs deployment on edge devices. However, prior SNN-based LLMs often sacrifice performance for efficiency, and recovering accuracy typically requires full pretraining, which is costly and impractical. To address this, we propose SpikingMamba, an energy-efficient SNN-based LLMs distilled from Mamba that improves energy efficiency with minimal accuracy sacrifice. SpikingMamba integrates two key components: (a) SI-LIF, a signed-integer spiking neuron that preserves semantic polarity through signed multi-level spike representations. (b) A training-exclusive Smoothed Gradient Compensation (SGC) path mitigating quantization loss while preserving spike-driven efficiency. We employ a single-stage distillation strategy to transfer the zero-shot ability of pretrained Mamba and further enhance it via reinforcement learning (RL). Experiments show that SpikingMamba-1.3B achieves a 4.76$\times$ energy benefit, with only a 4.78\% zero-shot accuracy gap compared to the original Mamba. The model achieves a further 2.55\% accuracy improvement after RL, narrowing the performance gap from 4.78\% to 2.23\%. Code is available at: https://github.com/HuuYuLong/SpikingMamba .

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