The results of the experimental and theoretical investigations aimed at determining the characteristics and features of precision slot cutting with a large number of calibers in sheets of low-carbon steel using the radiation of a single-mode fiber laser with pulse power up to 1 kW are presented. The description of the experimental installation, performance conditions of investigations, and variable parameters are described. Precision cutting of low-carbon steel up to 10 mm with the number of calibers ranging from 30 to 70 at a slot width of ≈60 μm is performed for the first time. Such cutting occurs only in the pulsed-periodic mode using single-mode radiation with a pulse duration of 2–3 ms, a pulse ratio of 2–4, and oxygen, whose influence differs in principle both in various cut regions over the sheet thickness and from cutting with a CO2 laser. The cutting velocity (100–50 mm/min) of sheet steel up to thicknesses of 10 mm with deep channeling, roughness parameters, hardness of the cut surface, which insignificantly (by ≈20%) exceeds the hardness of untreated steel, the phase structure of steel, and the scales of their varying inside metal are measured. The efficiency (≈3%) of precision cutting and the efficiency of transportation of radiation (25%) in large-caliber slot orifices in the “waveguide” mode are determined by the experimental data. The useful specific energy contribution of the laser radiation is wl = Nl/(hbv) ≈ 2 × 1012 J/m2 for all studied thicknesses of sheet samples accurate to 20%. A qualitative model of the laser-oxygen precision cutting with deep channeling, which explains the cyclic and interrupting character of cutting and necessity of using oxygen as the cutting gas, is proposed.