A newly developed Monte Carlo (MC) algorithm designed to study the complex interplay of dissolution and precipitation reactions on mineral surface is presented. This algorithm utilizes existing advanced reactive and configurational-biased MC techniques with new protocols specific for mineral-water interfaces. This time-independent methodology is especially advantageous for studying the kinetically slow quartz-water dissolution process. The aim is to use this method to understand the role of the local arrangement of reactive sites and surface topography in the surface evolution during dissolution. The simulations were performed in neutral pH medium, and two possible dissolution mechanisms were tested. The results indicate that out of the direct and stepwise mechanisms, the direct mechanism leads to complete dissolution that is not experimentally observed in the natural environment. On the other hand, the stepwise dissolution is more realistic, as it resembles the experimentally observed steady-state dissolution of the quartz-water system. These simulations identify the least coordinated surface sites (Q(1)) as the primary reactive site for hydrolysis and precipitation. Other surface sites (Q(2) and Q(3)) also undergo hydrolysis, but they are sterically hindered and are turned passive by precipitating Q(1) groups. The conclusions from the simulations are dominated by the surface topology of quartz; thus, we believe that the results are applicable for other polymorphs of silica and other protonation conditions.