Asymmetric sandwich technology serves as an effective option for introducing loads into sandwich structures in lieu of conventional inserts and joints in lightweight design of thin-walled aeronautical applications. In this study, buckling and failure behaviors are investigated on asymmetric sandwich panels with tapered regions subjected to shearing, where the panels are composed of CFRP laminates as skins and PMI foam as the core. Experimental data and observations are analyzed regarding critical loads, strain distributions, macro- and micro-scaled failure mechanisms. Detailed damage evolution is captured with the developed material and structural models. The influence of the core thickness on stability, load-bearing capacity and failure mechanisms is further investigated. Results show that the shear failure is mainly induced by buckling with an extensive matrix splitting fracture along the diagonal direction for sandwich panels with thin cores. Nonlinearity is observed in strain and deflection responses. Fiber pull-out is formed due to losing support of neighboring matrix. The fracture morphology of fiber breakage roughly appears oblique, indicating that the failure is mainly caused by the combination of tension and shearing. For sandwich panels with a thicker core, i.e. 10 mm and 12 mm, the failure mode switches to pure shear failure. Due to the intensification of tapered edges, local bugling occurs simultaneously with ultimate failure. The ultimate load presents a mounting-up and declining trend with the increase of core thickness, other than a monotonic trend. Conclusively, optimal design parameters exist, such as 10 mm core thickness in the studied case, regarding the load-bearing capacity.