Early detection of surgical complications allows for timely therapy and proactive risk mitigation. Machine learning (ML) can be leveraged to identify and predict patient risks for postoperative complications. We developed and validated the effectiveness of predicting postoperative complications using a novel surgical Variational Autoencoder (surgVAE) that uncovers intrinsic patterns via cross-task and cross-cohort presentation learning. This retrospective cohort study used data from the electronic health records of adult surgical patients over four years (2018 - 2021). Six key postoperative complications for cardiac surgery were assessed: acute kidney injury, atrial fibrillation, cardiac arrest, deep vein thrombosis or pulmonary embolism, blood transfusion, and other intraoperative cardiac events. We compared prediction performances of surgVAE against widely-used ML models and advanced representation learning and generative models under 5-fold cross-validation. 89,246 surgeries (49% male, median (IQR) age: 57 (45-69)) were included, with 6,502 in the targeted cardiac surgery cohort (61% male, median (IQR) age: 60 (53-70)). surgVAE demonstrated superior performance over existing ML solutions across all postoperative complications of cardiac surgery patients, achieving macro-averaged AUPRC of 0.409 and macro-averaged AUROC of 0.831, which were 3.4% and 3.7% higher, respectively, than the best alternative method (by AUPRC scores). Model interpretation using Integrated Gradients highlighted key risk factors based on preoperative variable importance. surgVAE showed excellent discriminatory performance for predicting postoperative complications and addressing the challenges of data complexity, small cohort sizes, and low-frequency positive events. surgVAE enables data-driven predictions of patient risks and prognosis while enhancing the interpretability of patient risk profiles.