Surface acoustic wave (SAW) devices based on multi-layer structures have been widely used in filters and sensors. The electromechanical coupling factor (K2), which reflects energy-conversion efficiency, directly determines the bandwidth of the filter and the sensitivity of sensor. In this work, a new configuration of dual-mode (quasi-Rayleigh and quasi-Sezawa) SAW devices on a ZnO/SiC layered structure exhibiting significantly enhanced K2 was studied using the finite element method (FEM), which features in the partial etching of the piezoelectric film between the adjacent interdigitated electrodes (IDTs). The influences of piezoelectric film thickness, etching ratio, top electrodes, bottom electrodes, and the metallization ratio on the K2 were systematically investigated. The optimum K2 for the quasi-Rayleigh mode and quasi-Sezawa mode can exceed 12% and 8%, respectively, which increases by nearly 12 times and 2 times that of the conventional ZnO/SiC structure. Such significantly promoted K2 is of great benefit for better comprehensive performance of SAW devices. More specifically, a quasi-Rayleigh mode with relatively low acoustic velocity (Vp) can be applied into the miniaturization of SAW devices, while a quasi-Sezawa mode exhibiting a Vp value higher than 5000 m/s is suitable for fabricating SAW devices requiring high frequency and large bandwidth. This novel structure has proposed a viable route for fabricating SAW devices with excellent overall performance.