All-metallic truncated conical sandwich shells with corrugated cores (TCSS) were investigated for crashworthiness under quasi-static oblique compression using a combined experimental and numerical approach. Subsequently, multi-objective optimization design of the TCSS was also performed by adopting the algorithm of NSGA-II to achieve maximum specific energy absorption (SEA) and minimum peak force ( ). Compared with a monolithic shell, the TCSS exhibits much higher SEA and lower under oblique loading, especially with its semi-apical angle set around 10° to 15°. The results provide valuable guidance for the application of truncated conical sandwich tubes in protective engineering, such as vehicle crashworthiness.