Research results of precision slot cutting in mild steel sheets (thickness up to 10 mm) using 1 kW power single-mode fiber laser were presented. In case of using pulse-repetition regime of single-mode fiber laser and oxygen, the number of slot calibers was achieved up to 70 (width of slot up to 60 pm). The cutting speed (100.50 mm/min), surface roughness, steel phase structure and hardness of cutting surface were measured. Efficiency (~3%) of precise cutting, transportation efficiency (25%) in waveguide regime was estimated. A qualitative model of the laser-oxygen cutting in case of large number calibers of slots was proposed.