Robust Unsupervised Domain Adaptation (RoUDA) aims to achieve not only clean but also robust cross-domain knowledge transfer from a labeled source domain to an unlabeled target domain. A number of works have been conducted by directly injecting adversarial training (AT) in UDA based on the self-training pipeline and then aiming to generate better adversarial examples (AEs) for AT. Despite the remarkable progress, these methods only focus on finding stronger AEs but neglect how to better learn from these AEs, thus leading to unsatisfied results. In this paper, we investigate robust UDA from a representation learning perspective and design a novel algorithm by utilizing the mutual information theory, dubbed MIRoUDA. Specifically, through mutual information optimization, MIRoUDA is designed to achieve three characteristics that are highly expected in robust UDA, i.e., robustness, discrimination, and generalization. We then propose a dual-model framework accordingly for robust UDA learning. Extensive experiments on various benchmarks verify the effectiveness of the proposed MIRoUDA, in which our method surpasses the state-of-the-arts by a large margin.