The high energy lasers are emerging as an innovative material processing tool to effectively fabricate complex shapes on the hard and brittle structural ceramics, which previously had been near impossible to be machined effectively using various conventional machining techniques. In addition, the in-situ measurement of the thermo-physical properties in the severe laser machining conditions (high temperature, short time duration, and small interaction volume) is an extremely difficult task. As a consequence, it is extremely challenging to investigate the evolution of surface topography through experimental analyses. To address this issue, an integrated experimental and computational (multistep and multiphysics based finite-element modeling) approach was employed to understand the influence of laser processing parameters to effectively control the various thermo-physical effects (recoil pressure, Marangoni convection, and surface tension) during transient physical processes (melting, vaporization) for controlled surface topography (surface finish). The results indicated that the material lost due to evaporation causes an increase in crater depth of machined cavity, whereas liquid expulsion created by the recoil pressure increases the material pileup height around the lip of machined cavity, the major attributes of surface topography (roughness). Also, it was found that the surface roughness increased with increase in laser energy density and pulse rate (from 10 to 50Hz), and with the decrease in distance between two pulses (from 0.6 to 0.1mm) or the increase in lateral and transverse overlap (0, 17, 33, 50, 67, and 83%). The results of the computational model are also validated by experimental observations with reasonably close agreement.