Solid-liquid separation plays an important role in many industrial fields. At present, efficient separation of solid particles from liquid is a problem when the density difference is small, and more efficient separation methods are required. Very recently, a new experimental approach was proposed for the solid-liquid separation in a stirred tank. This approach makes it possible to separate solid particles in a stirred tank. Although trajectory visualization methods of particles have been developed, the mechanism of the solid-liquid separation has not been well understood in the stirred system. In this study, we apply the numerical simulation of solid-liquid flows in a stirred vessel to examine the mechanism of solid-liquid separation. Previously, the numerical simulation of solid-liquid separation has not been performed so far. In this study, we use the DEM-CFD method in the simulation of solid-liquid flow in a stirred tank. The DEM-CFD method, which is combining the discrete element method (DEM) and computational fluid dynamics (CFD), is one of the standard approaches for the solid-fluid coupling simulation. In the numerical simulation, particles were initially dispersed in the vessel and then the paddle was rotated under laminar conditions. Clustering occurred immediately, and most of the particles moved into the isolated mixing regions. As a result, solid-liquid separation in the stirred system was observed even when the density difference between solid and liquid phases was small. Besides, in the tracking of particle trajectories, the clustered particles created helical orbits in the isolated mixing regions. Therefore, we found that particles moved into the isolated mixing regions and make helical orbits after clustering in the laminar stirred system. The resulting helical orbits have good agreements with those in existing experimental results. This indicates that the DEM-CFD method has a potential to reveal the solid-liquid separation mechanism in the stirred system. Consequently, numerical simulation was shown to be used for the better understanding of particle motions in stirred systems.