In this work, we show the damage induced by an intense coherent terahertz (THz) beam on copper surfaces. The metallic surface was irradiated by multiple picosecond THz pulses generated by the Free Electron Laser (FEL) at the ISIR facility of the Osaka University, reaching an electric field on the sample surface up to ~4 GV/m. No damage occurs at normal incidence, while images and spectroscopic analysis of the surface point out a clear dependence of the damage on the incidence angle, the electric field intensity, and polarization of the pulsed THz radiation. Ab initio analysis shows that the damage at high incidence angles could be related to the increase of the absorbance, i.e., to the increase of the temperature around or above 1000 °C. The experimental approach we introduced with multiple fast irradiations represents a new powerful technique useful to test, in a reproducible way, the damage induced by an intense electric gradient on copper and other metallic surfaces in view of future THz-based compact particle accelerators.