Previous works of negation understanding mainly focus on negation cue detection and scope resolution, without identifying negation subject which is also significant to the downstream tasks. In this paper, we propose a new negation triplet extraction (NTE) task which aims to extract negation subject along with negation cue and scope. To achieve NTE, we devise a novel Syntax&Semantic-Enhanced Negation Extraction model, namely SSENE, which is built based on a generative pretrained language model (PLM) {of Encoder-Decoder architecture} with a multi-task learning framework. Specifically, the given sentence's syntactic dependency tree is incorporated into the PLM's encoder to discover the correlations between the negation subject, cue and scope. Moreover, the semantic consistency between the sentence and the extracted triplet is ensured by an auxiliary task learning. Furthermore, we have constructed a high-quality Chinese dataset NegComment based on the users' reviews from the real-world platform of Meituan, upon which our evaluations show that SSENE achieves the best NTE performance compared to the baselines. Our ablation and case studies also demonstrate that incorporating the syntactic information helps the PLM's recognize the distant dependency between the subject and cue, and the auxiliary task learning is helpful to extract the negation triplets with more semantic consistency.