A mathematical model was developed to investigate the refining process through using slot-porous matched dual tuyeres. In this model, the bubble expansion is considered through the ideal gas state equation. The density variation of bubbles is calculated through the mass conservation equation. The coalescence and breakup of bubbles are tracked using the discrete particle model (DPM). The transient flow is computed through the k-ε model with three continuous phases (air–slag–steel). Comparisons were made between traditional porous–porous and the new slot–porous tuyeres, mainly focusing on the mixing behavior and inclusion removement ratio. The results show that, for traditional porous–porous matched tuyeres (P-P mode), the inclusion removement ratio is 34.14%; by comparison, after employing the slot–porous matched tuyeres (S-P mode), the inclusion removements ratio rises to 36.34%. The mixing time is also shortened by 18.74% by using the S-P mode. The reason for this phenomenon is because the slot tuyere produces a strong asymmetry that drives more liquid at the bottom of the ladle. The new tuyere match takes advantage of porous and slot tuyeres, and the mixing behavior and inclusion removements are improved. The result is beneficial for future refining.