The complexity of convolutional neural network architectures in hyperspectral image classification tasks results in long training times and high energy consumption, which severely limit the capabilities of edge computing equipment. To address the challenge of hyperspectral image classification in edge computing environments, we propose a spiking neural network (SNN) based on the hyperspectral classification method, which significantly reduces training time while maintaining high accuracy. Specifically, an approximate gradient algorithm is introduced to address the question of the non-differentiability of spike activity in spiking neurons. Subsequently, the method operates on channel and spatial dimensions, integrating a spatial–spectral attention mechanism to improve the capacity of the network to capture and simulate essential features. The proposed method is assessed using Pavia University, Indian Pines, and WHU-Hi hyperspectral datasets. The results indicate that the classification accuracy outperforms the models from spectral–spatial feature tokenization transformer (SSFTT), deep pyramidal residual networks (DPyResNet), small convolution and feature reuse (SC-FR) module, attention-based adaptive spectral–spatial kernel residual network (A2S2K-ResNet), and end-to-end spectral-spatial residual network (SSRN). It also reduces the training time by a factor of 7 for A2S2K-ResNet and 4 for SSRN. This algorithm presents an approach for deploying SNN models on edge devices, offering a fresh perspective for advancing hyperspectral image classification tasks.