Spiking neural networks (SNNs) are amenable to deployment on edge devices and neuromorphic hardware due to their lower dissipation. Recently, SNN-based transformers have garnered significant interest, incorporating attention mechanisms akin to their counterparts in artificial neural networks (ANNs) while demonstrating excellent performance. However, deploying large-scale spiking transformer models on resourceconstrained edge devices such as mobile devices still poses significant challenges resulting from the high computational demands of large uncompressed high-precision models. In this work, we introduce a novel heterogeneous quantization method to compress spiking transformers through layer-wise quantization. Our approach optimizes the quantization of each layer using one of two distinct quantization schemes, that is, uniform or power-of-two quantization, with mixed precision. Our heterogeneous quantization demonstrates the feasibility of maintaining high performance for spiking transformers while utilizing an average effective precision of 3.14-3.67 bits with less than a $\mathbf{1 \%}$ accuracy drop on neuromorphic DVS Gesture and CIFAR10-DVS datasets. It achieves $8.71 \times-10.19 \times$ model compression rate for standard floating-point spiking transformers. Furthermore, the proposed approach achieves substantial energy reductions of $5.69 \times, 8.72 \times$, and $10.2 \times$ on the N-Caltech101, DVS-Gesture, and CIFAR10DVS datasets, respectively, while maintaining high accuracy levels of $85.3 \%, 97.57 \%$, and 80.4 %.