The hydrodynamic damping of a buoy stationed with three different mooring configurations was estimated using a Navier-Stokes (NS) equations solver coupled with a dynamic mooring model. The mooring configurations comprised a catenary system, a catenary system with sub floaters, and a catenary system with sub floaters and clump weights. Systematic simulations were achieved by adopting the overset grid scheme instead of the conventional morphing grid scheme, which required regenerating the entire mesh when the buoy’s initial position changed, thereby avoiding mesh distortions and numerical instabilities. Motion decay simulations in heave, pitch, and surge were conducted with and without various mooring systems. The analyzed results comprised decaying oscillating motions, natural periods, and associated amounts of damping. The mooring systems influenced not only restoring force characteristics, but also total damping of the moored buoy, which demonstrated the importance of considering mooring-induced damping when investigating moored offshore structures.