Vision Transformers (ViTs) have demonstrated impressive performance across a range of applications, including many safety-critical tasks. However, their unique architectural properties raise new challenges and opportunities in adversarial robustness. In particular, we observe that adversarial examples crafted on ViTs exhibit higher transferability compared to those crafted on CNNs, suggesting that ViTs contain structural characteristics favorable for transferable attacks. In this work, we investigate the role of computational redundancy in ViTs and its impact on adversarial transferability. Unlike prior studies that aim to reduce computation for efficiency, we propose to exploit this redundancy to improve the quality and transferability of adversarial examples. Through a detailed analysis, we identify two forms of redundancy, including the data-level and model-level, that can be harnessed to amplify attack effectiveness. Building on this insight, we design a suite of techniques, including attention sparsity manipulation, attention head permutation, clean token regularization, ghost MoE diversification, and test-time adversarial training. Extensive experiments on the ImageNet-1k dataset validate the effectiveness of our approach, showing that our methods significantly outperform existing baselines in both transferability and generality across diverse model architectures.