Abstract Laser impact spot welding (LISW) is a relatively novel high-speed impact welding technology. It has obvious advantages in welding dissimilar metal foil plates which have a large difference in melting point. However, the bonding mechanism of laser impact spot welding and dynamic mechanical behavior during LISW are difficult to be revealed through experiments or theories. In this research, a systematic numerical simulation study of laser impact spot welding was conducted by using smooth particle hydrodynamics method. The results showed that the jet mainly originated from a thin layer of flyer plate (about 1 μm thick). It proved that the jet formation is an important condition for the solid-state welding. With the increase in impact velocity of the flyer plate, the bonding interface of Al/Cu and Ti/Cu became flat, tiny smooth wave and swirl-like wave, respectively. The local melting may occur when the impact velocity was large enough. In addition, the flyer plate would periodically penetrate the base plate under the combined action of impact pressure and shear stress, which would lead to the formation of bonding interface waves. Furthermore, the springback of the flyer plate and the spallation of the base plate were also simulated.