Evidence-aware fake news detection aims to determine the veracity of a given news (i.e., claim) with external evidences. We find that existing methods lack sufficient semantic perception and are easily blinded by textual expressions. For example, they still make the same prediction after we flip the semantics of a claim, which makes them vulnerable to malicious attacks. In this paper, we propose a model-agnostic training framework to improve the semantic perception of evidence-aware fake news detection. Specifically, we first introduce two kinds of data augmentation to complement the original training set with synthetic data. The semantic-flipped augmentation synthesizes claims with similar textual expressions but opposite semantics, while the semantic-invariant augmentation synthesizes claims with the same semantics but different writing styles. Moreover, we design a novel module to learn better claim representation which is more sensitive to the semantics, and further incorporate it into a multi-objective optimization paradigm. In the experiments, we also extend the original test set of benchmark datasets with the synthetic data to better evaluate the model perception of semantics. Experimental results demonstrate that our approach significantly outperforms the state-of-the-art methods on the extended test set, while achieving competitive performance on the original one. Our source code are released at https://github.com/Xyang1998/RobustFND.