Road-cut slopes in the Himalayan regions of India frequently experience the occurrence of rockfall hazards. These unfortunate events are mostly prevalent on jointed rock slopes having a vertical profile, and/or having one or more overhangs. In this study, a heavily jointed rock slope with an overhang along the National Highway 05 in the Kinnaur district of Himachal Pradesh has been analyzed under saturated conditions, and with persistent joints, using distinct element method in UDEC. Fragmentation of the overhang started from the beginning of calculation, and the rock block with the maximum velocity fell on the road section at approximately 61,229 cycles. Presence of vertical joints in the slope has been inferred to play a major role in the process. The mass of the rock block has been calculated to be 729 kg, and its impact energy at the time of contact with the ground is 49.8 kJ. The variation of kinetic energy of the falling block has been shown, along with conditions of the slope overhang after specific intervals of calculation cycles. The study has revealed that under saturated conditions, and in the occasion of incremental propagation of joints leading to increase in their average persistence, the overhang of the slope is highly unstable and hence, susceptible to fragmentation and subsequent fall of rock blocks on the road.