The hydrodynamics and stirring characteristics of the nitrogen-slag-copper matte in a bath with top submerged lance were numerically studied via the volume-of-fluid (VOF) method. The relationship between the bubble behavior and fluid velocity was elucidated. The effects of gas injecting velocity and swirling flow on the fluid vortex structure, gas penetration depth, and fluid velocity were investigated. The results demonstrate that the formation and rising of the bubble increase and reduce the fluid velocity, respectively. The V-shaped and W-shaped temperature distributions of the fluid are observed at the height of 0.43 and 0.52 m, respectively, resulting from the injection of the low-temperature gas phase. Compared to the gas injection velocity of 58 m/s, the time-averaged and maximum penetration depths of the gas phase with the injection velocity of 96 m/s increase by 78.4 % and 31.9 %, respectively. Swirling flow reduces the gas penetration depth, enhances the momentum transfer efficiency between phases, and suppresses the slag splashing, which is attributed to the reduced axial velocity component.