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 spiking transformer models on resource-constrained edge devices such as mobile phones, still poses significant challenges resulted from the high computational demands of large uncompressed high-precision models. In this work, we introduce a novel heterogeneous quantization method for compressing spiking transformers through layer-wise quantization. Our approach optimizes the quantization of each layer using one of two distinct quantization schemes, i.e., uniform or power-of-two quantification, with mixed bit resolutions. Our heterogeneous quantization demonstrates the feasibility of maintaining high performance for spiking transformers while utilizing an average effective resolution of 3.14-3.67 bits with less than a 1% accuracy drop on DVS Gesture and CIFAR10-DVS datasets. It attains a model compression rate of 8.71x-10.19x for standard floating-point spiking transformers. Moreover, the proposed approach achieves a significant energy reduction of 5.69x, 8.72x, and 10.2x while maintaining high accuracy levels of 85.3%, 97.57%, and 80.4% on N-Caltech101, DVS-Gesture, and CIFAR10-DVS datasets, respectively.