Spiking neural networks (SNNs) have revolutionized neural learning and are making remarkable strides in image analysis and robot control tasks with ultra-low power consumption advantages. Inspired by this success, we investigate the application of spiking neural networks to 3D point cloud processing. We present a point-to-spike residual learning network for point cloud classification, which operates on points with binary spikes rather than floating-point numbers. Specifically, we first design a spatial-aware kernel point spiking neuron to relate spiking generation to point position in 3D space. On this basis, we then design a 3D spiking residual block for effective feature learning based on spike sequences. By stacking the 3D spiking residual blocks, we build the point-to-spike residual classification network, which achieves low computation cost and low accuracy loss on two benchmark datasets, ModelNet40 and ScanObjectNN. Moreover, the classifier strikes a good balance between classification accuracy and biological characteristics, allowing us to explore the deployment of 3D processing to neuromorphic chips for developing energy-efficient 3D robotic perception systems.