Thermal cutting processes that can be applied to dismantling nuclear power plants include oxygen cutting, plasma cutting, and laser cutting. According to the global trend, research projects are being carried out in various countries to upgrade laser cutting, and many studies are also being conducted in Korea with plans to apply laser cutting processes when dismantling nuclear power plants. However, with the current technology level of the laser cutting process, the maximum thickness that can be cut is limited to 250 mm. Therefore, in this study, a laser-oxygen hybrid cutting process was implemented by adding a laser heat source to the oxygen cutting process that can cut carbon steel with a thickness of 250 mm or more (RV, beam, column, beam, etc.) when dismantling the nuclear power plant. This has the advantage of improving the cutting speed and reducing the cutting width Kerf compared to conventional oxygen cutting. In this research, the laser-oxygen hybrid cutting process consisted of laser cutting to which Raycus’ 8 kW Fiber Laser power source was applied and oxygen cutting to which hydrogen was applied with Fuel Gas. The oxygen torch was placed perpendicular to the test piece, and the laser head was irradiated by tilting 35° to 70°. The effects of cutting directions on quality and performance were studied, and cutting paths were selected by comparing cutting results. Thereafter, it was confirmed that there is an optimal laser output power according to the cutting thickness by studying the effect on the cutting surface quality by changing only the laser output power under the same cutting conditions. The results of this study are expected to be helpful in the remote cutting process using laser-oxygen hybrid cutting when dismantling domestic nuclear power plants in the future.