Aspect Sentiment Triplet Extraction (ASTE) aims to extract triplets from sentences, where each triplet includes an entity, its associated sentiment, and the opinion span explaining the reason for the sentiment. Most existing research addresses this problem in a multi-stage pipeline manner, which neglects the mutual information between such three elements and has the problem of error propagation. In this paper, we propose a Semantic and Syntactic Enhanced aspect Sentiment triplet Extraction model (S3E2) to fully exploit the syntactic and semantic relationships between the triplet elements and jointly extract them. Specifically, we design a Graph-Sequence duel representation and modeling paradigm for the task of ASTE: we represent the semantic and syntactic relationships between word pairs in a sentence by graph and encode it by Graph Neural Networks (GNNs), as well as modeling the original sentence by LSTM to preserve the sequential information. Under this setting, we further apply a more efficient inference strategy for the extraction of triplets. Extensive evaluations on four benchmark datasets show that S3E2 significantly outperforms existing approaches, which proves our S3E2's superiority and flexibility in an end-to-end fashion.