Real-world graphs or networks are usually heterogeneous, involving multiple types of nodes and relationships. Heterogeneous graph neural networks (HGNNs) can effectively handle these diverse nodes and edges, capturing heterogeneous information within the graph, thus exhibiting outstanding performance. However, most methods of HGNNs usually involve complex structural designs, leading to problems such as high memory usage, long inference time, and extensive consumption of computing resources. These limitations pose certain challenges for the practical application of HGNNs, especially for resource-constrained devices. To mitigate this issue, we propose the Spiking Heterogeneous Graph Attention Networks (SpikingHAN), which incorporates the brain-inspired and energy-saving properties of Spiking Neural Networks (SNNs) into heterogeneous graph learning to reduce the computing cost without compromising the performance. Specifically, SpikingHAN aggregates metapath-based neighbor information using a single-layer graph convolution with shared parameters. It then employs a semantic-level attention mechanism to capture the importance of different meta-paths and performs semantic aggregation. Finally, it encodes the heterogeneous information into a spike sequence through SNNs, simulating bioinformatic processing to derive a binarized 1-bit representation of the heterogeneous graph. Comprehensive experimental results from three real-world heterogeneous graph datasets show that SpikingHAN delivers competitive node classification performance. It achieves this with fewer parameters, quicker inference, reduced memory usage, and lower energy consumption. Code is available at https://github.com/QianPeng369/SpikingHAN.