In laser cutting, the auxiliary gas and laser beam axis are typically coaxially arranged to ensure the same cutting quality in each cutting direction. It is found that when the axes of the auxiliary gas and laser beam are not coaxial (i.e., in an off-axis state), the cutting efficiency can be effectively improved. However, the influence mechanism of off-axis state on the cutting process remains unclear. This study established a three-dimensional symmetrical model of off-axis laser cutting with cut slits and simulated the laser cutting process with nitrogen as the auxiliary gas using the finite element method. By changing the off-axis amount, the structure of the airflow field structure of the auxiliary gas is analyzed, meanwhile, the influence of the off-axis amount on the dynamic performance of the auxiliary gas was investigated during the laser cutting process. In addition, the influence mechanism of the off-axis amount on the laser cutting was clarified by analyzing the simulation results, and it was verified in a cutting experiment. Results show that the off-axis amount affects the dynamic performance of the auxiliary gas, and the appropriate off-axis amount can effectively improve the quality of laser cutting.