To optimize optical coating materials, designs, and technologies for high damage resistance, understanding the growth of laser damage is of paramount importance. In this Letter, we show the evolution of femtosecond laser damage in a hafnia-silica (HfO2/SiO2) multilayer dielectric mirror coating. Depending on various spatial features of damaged sites, we identified several regimes of the laser-material interaction with varying laser fluence and incident number of pulses. A change in surface roughness has been observed only for a small number of pulses, and interestingly, a threshold number of pulses is found for nanocrack formation. We report the polarization-dependent orientation of nanocracks and their growth with an increasing number of pulses. The presented results demonstrate that the laser damage originates from the nanobumps and surface roughening, which then leads to the formation of nanocracks. The presented experimental results acknowledge the existing theoretical models in bulk dielectrics to explain the formation of nanostructures by interference of the incident laser with the scattering radiation from laser-induced inhomogeneities and growth of the field enhancement due to nanoplasma.