Although wind turbine installation vessels (WTIVs) are increasingly operating in deepwater complex geological areas with larger scales, systematic research on and experimental validation of platform jack-up stability remain insufficient. This study aimed to establish a comprehensive evaluation framework encompassing penetration depth, anti-overturning/sliding stability, and punch-through risk, thereby filling the gap in holistic platform stability analysis. An entire four-legged centrifuge test at 150× g was integrated with coupled Eulerian–Lagrangian (CEL) numerical simulations and theoretical methods to systematically investigate spudcan penetration mechanisms and global sliding/overturning evolution in clay/sand. The key findings reveal that soil properties critically influence penetration resistance and platform stability: Sand exhibited a six-times-higher ultimate bearing capacity than clay, yet its failure zone was 42% smaller. The sliding resistance in sand was 2–5 times greater than in clay, while the overturning behavior diverged significantly. Although the horizontal loads in clay were only 50% of those in sand, the tilt angles at equivalent sliding distances reached 8–10 times higher. Field validation at Guangdong Lemen Wind Farm confirmed the method’s reliability: penetration prediction errors of <5% and soil backflow/plugging effects were identified as critical control factors for punch-through risk assessment. Notably, the overturning safety factors for crane operation at 90° outreach and storm survival were equivalent, indicating operational load combinations dominate overturning risks. These results provide a theoretical and decision-making basis for the safe operation of large WTIVs, particularly applicable to engineering practices in complex stratified seabed areas.