In this experiment, a quaternary fluorine-free refining slag system of CaO-SiO2-Al2O3-MgO was selected, with basicity ratios of 2, 4, and 6 and calcium-aluminum ratios of 1.5, 2.1, and 3. High-temperature “slag-steel equilibrium” experiments were conducted to investigate the influence of different basicity ratios and calcium–aluminum ratios on the morphologies, compositions, sizes, and quantities of the inclusions in H13 steel, aiming to improve the cleanliness of H13 steel to meet practical industrial requirements. The experimental results showed that with the increase in the basicity ratio and the calcium–aluminum ratio, the morphologies of the inclusions changed from elliptical to regular circular, with more regular edges. As the basicity ratio increased from 2 to 6, the densities of the inclusions showed a decreasing trend, with values of 40, 35, 30, 25, 32, and 30 inclusions/mm2. When the basicity ratio remained the same, the average size of the inclusions in the steel decreased first and then increased with the increases in the calcium–aluminum ratios, with sizes of 1.59 μm, 1.23 μm, and 1.38 μm, respectively. Among these, when the basicity ratio was 6 and the calcium–aluminum ratio was 2.1, the control effect on the densities and sizes of the inclusions was the best, yielding an inclusion density of 25 inclusions/mm2 and a size of 1.15 μm. Additionally, reducing the Al2O3 content in the slag could reduce the Al2O3 contents in the inclusions, which also promoted improvements in the elastic deformation capacities of the inclusions. With increases in the calcium–aluminum ratios in the slag system, the masses of the inclusions decreased due to the reduced Al contents in the steel. The Al contents in the steel also had an impact on the compositions of the inclusions.