Spiking neural networks (SNNs) have attracted considerable attention as third-generation artificial neural networks, known for their powerful, intelligent features and energy-efficiency advantages. These characteristics render them ideally suited for edge computing scenarios. Nevertheless, the current mapping schemes for deploying SNNs onto neuromorphic hardware face limitations such as extended execution times, low throughput, and insufficient consideration of energy consumption and connectivity, which undermine their suitability for edge computing applications. To address these challenges, we introduce EdgeMap, an optimized mapping toolchain specifically designed for deploying SNNs onto edge devices without compromising performance. EdgeMap consists of two main stages. The first stage involves partitioning the SNN graph into small neuron clusters based on the streaming graph partition algorithm, with the sizes of neuron clusters limited by the physical neuron cores. In the subsequent mapping stage, we adopt a multi-objective optimization algorithm specifically geared towards mitigating energy costs and communication costs for efficient deployment. EdgeMap—evaluated across four typical SNN applications—substantially outperforms other state-of-the-art mapping schemes. The performance improvements include a reduction in average latency by up to 19.8%, energy consumption by 57%, and communication cost by 58%. Moreover, EdgeMap exhibits an impressive enhancement in execution time by a factor of 1225.44×, alongside a throughput increase of up to 4.02×. These results highlight EdgeMap’s efficiency and effectiveness, emphasizing its utility for deploying SNN applications in edge computing scenarios.