Severe acute pancreatitis (SAP) is a heterogeneous and potentially fatal disease in which infected necrosis, persistent organ failure, and procedure-related morbidity remain major clinical challenges. Although minimally invasive intervention has largely replaced early open necrosectomy, important uncertainties persist regarding the optimal timing of intervention, the choice of initial access route, and the threshold for escalation beyond drainage alone. This review synthesizes current evidence on minimally invasive management of SAP with a particular focus on unresolved controversies and decision-making in real-world practice. Rather than viewing percutaneous, endoscopic, and minimally invasive surgical techniques as competing modalities, we propose that they should be understood as complementary tools within an individualized step-up strategy. In our view, the most meaningful clinical question is not whether minimally invasive treatment is preferable to open surgery, but how intervention should be tailored according to indication, urgency, collection maturity, anatomical distribution, solid necrotic burden, septic trajectory, and local multidisciplinary expertise. Based on these considerations, we present a practical decision-centered framework to guide route selection, timing, and escalation. Future research should move beyond broad modality comparisons toward anatomy-stratified studies, standardized escalation criteria, and long-term patient-centered outcomes.