Several recent works have shown that giant planet growth and migration can play an important role in shaping the asteroid belt, but these works have not considered the effects of interactions between planetesimals. We have calculated the evolution of planetesimal disks, including planetesimal-planetesimal impacts, during the periods of gas giant growth and migration. The numbers and impact velocities of these collisions, and when and where they occur, depend on the specific growth and migration path. Giant planet migration induces large numbers of high velocity collisions between planetesimals. These impacts have sufficient velocities to cause shock-induced vaporization for both water ice and silicate components of planetesimals, and to cause catastrophic disruption of the bodies. Collisional evolution reduces the efficiency of planetesimal implantation into the asteroid belt via giant planet growth and migration. The prevalence of high velocity collisions during giant planet migration, and their potential links to the observed properties of meteorites, and the formation of chondrules, makes impact vaporization in planetesimals a critically important phenomenon.