We report on the development of a mitigation process to prevent the growth of UV nanosecond laser-initiated damage sites under successive irradiations of fused silica components. The developed process is based on fast microablation of silica as it has been proposed by Bass et al. [Bass et al., Proc. SPIE 7842, 784220 (2010)]. This is accomplished by the displacement of the laser spot with a fast galvanometer beam scanner to form a crater with a typical conical shape to mitigate large (millimetric) and deep (few hundred microns) damage sites. We present the developed experimental system and process for this application. Particularly, we detail and evaluate a method based on quantitative phase imaging to obtain fast and accurate three-dimensional topographies of the craters. The morphologies obtained through different processes are then studied. Mitigation of submillimetric nanosecond damage sites is demonstrated through different examples. Experimental and numerical studies of the downstream intensifications, resulting in cone formation on the surface, are presented to evaluate and minimize the downstream intensifications. Eventually, the laser damage test resistance of the mitigated sites is evaluated at 355, 2.5 ns, and we discuss on the efficiency of the process for our application.