We investigate the robustness of vision transformers (ViTs) through the lens of their special patch-based architectural structure, i.e., they process an image as a sequence of image patches. We find that ViTs are surprisingly insensitive to patch-based transformations, even when the transformation largely destroys the original semantics and makes the image unrecognizable by humans. This indicates that ViTs heavily use features that survived such transformations but are generally not indicative of the semantic class to humans. Further investigations show that these features are useful but non-robust, as ViTs trained on them can achieve high in-distribution accuracy, but break down under distribution shifts. Based on this understanding, we use the images transformed with our patch-based operations as negatively augmented views and offer losses to regularize the training away from using non-robust features. This is a complementary view to existing research that mostly focuses on augmenting inputs with semantic-preserving transformations to enforce models' invariance.We show that patch-based negative augmentation consistently improves robustness of ViTs across a wide set of ImageNet based robustness benchmarks. Furthermore, we find our patch-based negative augmentation are complementary to traditional (positive) data augmentation, and together boost the performance further. All the codes in this work will be open-sourced.