Sarcasm thrives on popular social media platforms such as Twitter and Reddit, where users frequently employ it to convey emotions in an ironic or satirical manner. The ability to detect sarcasm plays a pivotal role in comprehending individuals’ true sentiments. To achieve a comprehensive grasp of sentence semantics, it is crucial to integrate external knowledge that can aid in deciphering entities and their intricate relationships within a sentence. Although some efforts have been made in this regard, their use of external knowledge is still relatively superficial. Specifically, Knowledge-enhanced entity and relationship understanding still face significant challenges. In this paper, we propose the Knowledge Enhanced Sentiment Dependency Graph Convolutional Network (KSDGCN) framework, which constructs a commonsense-augmented sentiment graph and a commonsense-replaced dependency graph for each text to explicitly capture the role of external knowledge for sarcasm detection. Furthermore, we validate the irrational relationships between co-occurring entity pairs within sentences and background knowledge by a signed attention mechanism. We conduct experiments on four benchmark datasets, and the results show that KSDGCN outperforms existing state-of-the-art methods and is highly interpretable.