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While deep learning demonstrates its strong ability to handle independent and identically distributed (IID) data, it often suffers from out-of-distribution (OoD) generalization, where the test data come from another distribution (w.r.t. the training one). Designing a general OoD generalization framework to a wide range of applications is challenging, mainly due to possible correlation shift and diversity shift in the real world. Most of the previous approaches can only solve one specific distribution shift, such as shift across domains or the extrapolation of correlation. To address that, we propose DecAug, a novel decomposed feature representation and semantic augmentation approach for OoD generalization. DecAug disentangles the category-related and context-related features. Category-related features contain causal information of the target object, while context-related features describe the attributes, styles, backgrounds, or scenes, causing distribution shifts between training and test data. The decomposition is achieved by orthogonalizing the two gradients (w.r.t. intermediate features) of losses for predicting category and context labels. Furthermore, we perform gradient-based augmentation on context-related features to improve the robustness of the learned representations. Experimental results show that DecAug outperforms other state-of-the-art methods on various OoD datasets, which is among the very few methods that can deal with different types of OoD generalization challenges.