PETAL (PETawatt Aquitaine Laser) is an ultra-highpower laser dedicated to academic research that delivers sub-picosecond pulses. One of the major issues on these facilities is the laser damage on optical components located at the final stage. Transport mirrors of the PETAL facility are illuminated under different polarization directions. This configuration motivates thorough investigation of the dependency of the laser damage growth features (thresholds, dynamics and damage site morphologies) with the incident polarization. Damage growth experiments were carried out in s and p-polarization at 0.8 ps and 1053 nm on multilayer dielectric mirrors with a squared top-hat beam. Damage growth coefficients are determined by measuring the evolution of the damaged area for both polarizations. In this paper, we report higher damage growth threshold in p-polarization together with higher damage initiation threshold in s-polarization. We also report faster damage growth dynamics in p-polarization. The damage site morphologies and their evolution under successive pulses are found to strongly depend on polarization. A numerical model in 3D was developed to assess this experimental observations, it shows the relative differences in damage growth threshold however, it was not able to reproduce the damage growth rate. Numerical results demonstrate that damage growth is mainly driven by the electric field distribution which depends on the polarization.