Surface electromyography (sEMG) based gesture recognition offers a natural and intuitive interaction modality for wearable devices. Despite significant advancements in sEMG-based gesture-recognition models, existing methods often suffer from high computational latency and increased energy consumption. Additionally, the inherent instability of sEMG signals, combined with their sensitivity to distribution shifts in real-world settings, compromises model robustness. To tackle these challenges, we propose a novel SpGesture framework based on Spiking Neural Networks, which possesses several unique merits compared with existing methods: (1) Robustness: By utilizing membrane potential as a memory list, we pioneer the introduction of Source-Free Domain Adaptation into SNN for the first time. This enables SpGesture to mitigate the accuracy degradation caused by distribution shifts. (2) High Accuracy: With a novel Spiking Jaccard Attention, SpGesture enhances the SNNs' ability to represent sEMG features, leading to a notable rise in system accuracy. To validate SpGesture's performance, we collected a new sEMG gesture dataset which has different forearm postures, where SpGesture achieved the highest accuracy among the baselines ($89.26\%$). Moreover, the actual deployment on the CPU demonstrated a system latency below 100ms, well within real-time requirements. This impressive performance showcases SpGesture's potential to enhance the applicability of sEMG in real-world scenarios. The code is available at https://github.com/guoweiyu/SpGesture/.