Multilayer structured REBCO coated conductor (CC) tapes undergo various types of stress and strain when used in superconducting devices like high-field magnets and coils. One of the stresses they experience is radial transverse tensile ones arising from the Lorentz force. This stress can cause delamination damage to the CC tapes’ intricate layered structures and interfaces, compromising their integrity and leading to the superconducting device's catastrophic failure. The stabilizing layers in REBCO CC tapes maintain their structural integrity and prevent delamination damage. Multilayered REBCO CC tapes are characterized by a significant scattering of measured delamination strength. This requires establishing a standard test method for measuring the delamination strength of CC tapes, and various efforts are being carried out to establish a reliable test method. On the other hand, the role of the Cu layer stabilizer in binding together the different components with varying properties, particularly the coefficient of thermal expansion (CTE), should be investigated. The Cu stabilizer ensures the CC tape remains structurally stable against transversely applied external forces during fabrication and application. However, the specific role of Cu layers at the edge parts of the CC tapes, particularly in their contribution to delamination resistance, is not yet fully understood. We conducted a comprehensive study of experimental delamination testing and numerical simulation to address this critical research gap. We investigated the mechanical and electromechanical delamination strength of REBCO CC tape with different thicknesses of Cu stabilizer, comparing the cases with Cu-edge to those without Cu layer at edges. Additionally, we performed numerical simulations of the same configuration adopted in the experiment to understand how the Cu layer at the edge affects the stress distribution at the interfaces during the anvil test. Through this meticulous analysis, we aim to establish a reliable delamination test method for REBCO CC tapes and standardization. This knowledge will also provide valuable insights for optimizing the design and fabrication of these vital components, leading to the development of more robust and reliable superconducting devices. This work was supported by a Korea Planning & Evaluation Institute of Industrial Technology (KEIT) grant funded by the Korean Government (MOTIE) (Grant No. RS-2024-00435492). It was also partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2022M3I9A1076881).