Argument pair extraction (APE) is a task that aims to extract interactive argument pairs from two argument passages. Generally, existing works focus on either simple argument interaction or task form conversion, instead of thorough deep-level feature exploitation of argument pairs. To address this issue, a Semantics-Aware Dual Graph Convolutional Networks (SADGCN) is proposed for APE. Specifically, the co-occurring word graph is designed to tackle the lexical and semantic relevance of arguments with a pre-trained Rouge-guided Transformer (ROT). Considering the topic relevance in argument pairs, a topic graph is constructed by the neural topic model to leverage the topic information of argument passages. The two graphs are fused via a gating mechanism, which contributes to the extraction of argument pairs. Experimental results indicate that our approach achieves the state-of-the-art performance. The performance on F1 score is significantly improved by 6.56% against the existing best alternative.