A numerical study has been conducted to investigate the interaction of two viscous vortex rings along parallel axes. The generation of two vortex rings created by the ejection of a fluid through orifices and their cut-and-connect process were numerically simulated by solving the three-dimensional and time-dependent Navier-Stokes equations. Based on the quantitative velocity and pressure data obtained from the Navier-Stokes simulation, the distribution and the evolution of the vorticity, helicity density and energy dissipation function were analyzed. The helicity density and its relation with the energy dissipation function in three-dimensional flow fields were also examined. It was found that the energy dissipation plays an important role in the cancellation of the vortex circulation during the vortex tubes cutting. This energy dissipation process may be used to explain the cut-and-connect of vortex tubes in the high Reynolds number turbulent flow. The numerical solutions were compared with the experimental observations and measurements under the similar condition. The correspondence between the numerical simulation and the experimental measurement was satisfactory.