Open-set domain adaptation (OSDA) considers that the target domain contains samples from novel categories unobserved in external source domain. Unfortunately, existing OSDA methods always ignore the demand for the information of unseen categories and simply recognize them as "unknown" set without further explanation. This motivates us to understand the unknown categories more specifically by exploring the underlying structures and recovering their interpretable semantic attributes. In this paper, we propose a novel framework to accurately identify the seen categories in target domain, and effectively recover the semantic attributes for unseen categories. Specifically, structure preserving partial alignment is developed to recognize the seen categories through domain-invariant feature learning. Attribute propagation over visual graph is designed to smoothly transit attributes from seen to unseen categories via visual-semantic mapping. Moreover, two new cross-main benchmarks are constructed to evaluate the proposed framework in the novel and practical challenge. Experimental results on open-set recognition and semantic recovery demonstrate the superiority of the proposed method over other compared baselines.