Unsupervised domain adaptation (UDA) aims to address the domain-shift problem between a labeled source domain and an unlabeled target domain. Many efforts have been made to eliminate the mismatch between the distributions of training and testing data by learning domain-invariant representations. However, the learned representations are usually not task-oriented, i.e., being class-discriminative and domain-transferable simultaneously. This drawback limits the flexibility of UDA in complicated open-set tasks where no labels are shared between domains. In this paper, we break the concept of task-orientation into task-relevance and task-irrelevance, and propose a dynamic task-oriented disentangling network (DTDN) to learn disentangled representations in an end-to-end fashion for UDA. The dynamic disentangling network effectively disentangles data representations into two components: the task-relevant ones embedding critical information associated with the task across domains, and the task-irrelevant ones with the remaining non-transferable or disturbing information. These two components are regularized by a group of task-specific objective functions across domains. Such regularization explicitly encourages disentangling and avoids the use of generative models or decoders. Experiments in complicated, open-set scenarios (retrieval tasks) and empirical benchmarks (classification tasks) demonstrate that the proposed method captures rich disentangled information and achieves superior performance.