The prevalence and perniciousness of fake news have been a critical issue on the Internet, which stimulates the development of automatic fake news detection in turn. In this paper, we focus on the evidence-based fake news detection, where several evidences are utilized to probe the veracity of news (i.e., a claim). Most previous methods first employ sequential models to embed the semantic information and then capture the claim-evidence interaction based on different attention mechanisms. Despite their effectiveness, they still suffer from three weaknesses. Firstly, due to the inherent drawbacks of sequential models, they fail to integrate the relevant information that is scattered far apart in evidences for veracity checking. Secondly, they underestimate much redundant information contained in evidences that may be useless or even harmful. Thirdly, insufficient data utilization limits the separability and reliability of representations captured by the model, which are sensitive to local evidence. To solve these problems, we propose a unified G raph-based s E mantic structure mining framework with Con TRA stive L earning, namely GETRAL in short. Specifically, different from the existing work that treats claims and evidences as sequences, we first model them as graph-structured data and capture the long-distance semantic dependency among dispersed relevant snippets via neighborhood propagation. After obtaining contextual semantic information, our model reduces information redundancy by performing graph structure learning. Then the fine-grained semantic representations are fed into the downstream claim-evidence interaction module for predictions. Finally, the supervised contrastive learning accompanied with adversarial augmented instances is applied to make full use of data and strengthen the representation learning. Comprehensive experiments have demonstrated the superiority of GETRAL over the state-of-the-arts and validated the efficacy of semantic mining with graph structure and contrastive learning.