Sepsis is a major cause of ICU mortality, where early recognition and effective interventions are essential for improving patient outcomes. However, the vasoactive-inotropic score (VIS) varies dynamically with a patient's hemodynamic status, complicated by irregular medication patterns, missing data, and confounders, making sepsis prediction challenging. To address this, we propose a novel Teacher-Student multitask framework with self-supervised VIS pretraining via a Masked Autoencoder (MAE). The teacher model performs mortality classification and severity-score regression, while the student distills robust time-series representations, enhancing adaptation to heterogeneous VIS data. Compared to LSTM-based methods, our approach achieves an AUROC of 0.82 on MIMIC-IV 3.0 (9,476 patients), outperforming the baseline (0.74). SHAP analysis revealed that SOFA score (0.147) had the greatest impact on ICU mortality, followed by LODS (0.033), single marital status (0.031), and Medicaid insurance (0.023), highlighting the role of sociodemographic factors. SAPSII (0.020) also contributed significantly. These findings suggest that both clinical and social factors should be considered in ICU decision-making. Our novel multitask and distillation strategies enable earlier identification of high-risk patients, improving prediction accuracy and disease management, offering new tools for ICU decision support.