Effects of peak stress on the properties of dynamic damage evolution of oxygen free high-pure copper (OFHC) are investigated. The spall fracture experiments are conducted in gas gun, and the damage evolution process is studied using the time-resolved free-surface velocity interferometry, also the post-experiment metallurgical analysis of the soft-recovered samples. It is indicated that, with the increase of peak stress, the spall strength has little changed, but distinct differences are observed in the magnitude and rate of damage at which the velocity rises to the first peak beyond the minima, and the rate of damage evolution increases remarkably. It is concluded that the peak stress is not sensitive to the nucleation of voids, but is one of the most important factors for the growth of voids.