In this paper, we describe the design and manufacturing of a viscous inertial mass-damper (VIMD) prototype. The damper parameters, the inertial mass, and the viscous damping coefficient can be continuously adjusted. Experimental validations were carried out on the VIMD with various parameters and a scaled sagged cable of 19.47 m long with the VIMD for vibration mitigation, along with a simulation study using the finite element method (FEM). The experimental results show that the modal damping ratio of the scaled cable was remarkably increased by the VIMD. The achieved maximum modal damping ratios for the first two modes were 6.98% and 8.15%, respectively, which are about 10 times the maximum values using a conventional viscous damper. The sag influence on damper-control performance was also studied by changing the cable tension. It showed that the first modal damping ratio provided by the VIMD was significantly reduced by the increased sag, whereas the second modal damping ratio was not. Fourier amplitude spectra of the cable responses subjected to sine sweep excitations show that the cable mode split into two and a pair of fixed points occurred by introducing a VIMD as in the theory of the fixed-point method (FPM) for the optimum design of a tuned mass damper. The performance of the optimum VIMD by the FPM was investigated in comparison with that by the maximum modal damping method.