In this paper, the relationship between various physical and chemical dynamics included in a gas cutting process was analyzed and a mathematical model was presented. To express the gas cutting process in a formula that could reflect the physics and chemical reaction dynamics, the entire process was classified into three stages: flame spurt, metal oxidation, and metal oxide melting. Flame spurt is caused by combustion of fuel gas and oxygen. It was modeled through fluid dynamics, chemical species transport, and reaction kinetics. Metal oxidation was modeled as a chemical reaction of surface oxidation and oxide growth based on temperature and concentration of species of the metal surface obtained through flame and cutting oxygen spurt results. Finally, the melting of metal oxide was expressed as a rate equation based on melting conditions, heat flux obtained in the previous two stages, and changed properties of the metal. The presented mathematical model could analyze dynamic relationships for each stage of a gas cutting process and connect them into one process. Results of this study can be used as basic data for future finite element analysis and simulations.