Stainless steel 304 is one of the most commonly used steel types for corrosion resistance applications, but higher melting point is a limitation in industries from a manufacturing point of view. The non-conventional and subtractive manufacturing technique of laser cutting — a beam directed method, is suitable for these applications. A Gaussian laser beam is directed at the material that melts, burns, vaporizes, or is blown away by a jet of gas, leaving a fine edge with good surface finish. In this study, a numerical study was performed to study the multi-physical fluid processes of laser cutting. Towards this, modeling was performed using 1.2 mm thick austenitic stainless-steel coupons that was cut using a continuous width neodymium-doped yttrium aluminum garnet (CW Nd: YAG) laser. The results showed smoother surface cut, little dross formation, lower temperature rise in heat affected zones, and less finish time at a cutting speed of 8m/min, higher laser power above 1000 W, gas pressure of 11 bars, and focus distance of −1.0 mm. It was observed that an increase in laser power at a faster cutting speed led to an increase in kerf width, reduction in dross formation, lower temperature rises in heat affected zones and a reduced finish time. The simulation results were compared with published experimental data and found to be well within a maximum difference of 15%.