With the growing sizes of AI models like large language models (LLMs) and vision transformers, deploying them on devices with limited computational resources is a challenge particularly when addressing domain generalisation (DG) tasks. This paper introduces a novel grouped structural pruning method for pre-trained vision transformers (ViT, BEIT, and DEIT), evaluated on the PACS and Office-Home DG benchmarks. Our method uses dependency graph analysis to identify and remove redundant groups of neurons, weights, filters, or attention heads within transformers, using a range of selection metrics. Grouped structural pruning is applied to reduce model sizes at pruning ratios of 50%, 75% and 95% and the models are fine-tuned on selected distributions from DG benchmarks to evaluate their overall performance in DG tasks. Results show significant improvements in inference speed and fine-tuning time with minimal trade-offs in accuracy and DG task performance. For instance, on the PACS benchmark, pruning ViT, BEIT, and DEIT models by 50% using the Hessian metric resulted in accuracy drops of only -2.94%, -1.42%, and -1.72%, respectively, while achieving speed boosts of 2.5x, 1.81x, and 2.15x. These findings demonstrate the effectiveness of our approach in balancing model efficiency with domain generalisation performance.