Along with predictive performance and runtime speed, robustness is a key requirement for real-world semantic segmentation. Robustness encompasses accuracy, predictive uncertainty, stability under data perturbation and distribution shift, and reduced bias. To improve robustness, we introduce Superpixel-mix, a new superpixel-based data augmentation method with teacher-student consistency training. Unlike other mixing-based augmentation techniques, mixing superpixels between images is aware of object boundaries, while yielding consistent gains in segmentation accuracy. Our proposed technique achieves state-of-the-art results in semi-supervised semantic segmentation on the Cityscapes dataset. Moreover, Superpixel-mix improves the robustness of semantic segmentation by reducing network uncertainty and bias, as confirmed by competitive results under strong distributions shift (adverse weather, image corruptions) and when facing out-of-distribution data.