Open Set Domain Adaptation (OSDA) transfers the model from a label-rich domain to a label-free one containing novel-class samples. Existing OSDA works overlook abundant novel-class semantics hidden in the source domain, leading to a biased model learning and transfer. Although the causality has been studied to remove the semantic-level bias, the non-available novel-class samples result in the failure of existing causal solutions in OSDA. To break through this barrier, we propose a novel causality-driven solution with the unexplored front-door adjustment theory, and then implement it with a theoretically grounded framework, coined AdjustmeNt aNd Alignment (ANNA), to achieve an unbiased OSDA. In a nutshell, ANNA consists of Front-Door Adjustment (FDA) to correct the biased learning in the source domain and Decoupled Causal Alignment (DCA) to transfer the model unbiasedly. On the one hand, FDA delves into fine-grained visual blocks to discover novel-class regions hidden in the base-class image. Then, it corrects the biased model optimization by implementing causal debiasing. On the other hand, DCA disentangles the base-class and novel-class regions with orthogonal masks, and then adapts the decoupled distribution for an unbiased model transfer. Extensive experiments show that ANNA achieves state-of-the-art results. The code is available at https://github.com/CityU-AIM-Group/Anna.