The thick copper stainless steel composite plate is an important component of the cooling coil terminal box of international nuclear fusion reactors. The composite rate, tensile strength, shear strength, and interface waveform of the metal plate are also far higher than the requirements of conventional explosive welding technology. It is difficult to obtain the best technical process parameters in a short time solely relying on conventional explosive welding tests. In order to solve the above-mentioned technical difficulties in explosive welding, this article applies the generalized interpolation material point method (GIMP) based on the explosive welding window, metal elastic-plastic mechanics, and explosive detonation theory to conduct macroscopic three-dimensional and microscopic two-dimensional numerical simulations of the copper stainless steel explosive welding process and the composite interface wave formation process, respectively. The experimental results demonstrate that the GIMP has significant advantages in numerical calculation and analysis for the explosive welding problem of high-speed impact collision of metal plates driven by explosive detonation, and it can effectively solve the technical problems of high technical specifications, low explosive processing composite rate, and low interface strength of large thickness copper stainless steel composite plates used in nuclear fusion.