Although various technologies, including nuclear explosions, kinetic impactors, and slow- pull gravity tractors, have been proposed for mitigating the impact threat of near-Earth objects (NEOs), there is no consensus on how to reliably deflect or disrupt such hazardous NEOs in a timely manner. This paper describes the orbital dispersion modeling, analysis, and simulation of an NEO fragmented and dispersed by nuclear subsurface explosions. It is shown that various fundamental approaches of Keplerian orbital dynamics can be effectively employed for the orbital dispersion analysis of fragmented NEOs. This paper also shows that, under certain conditions, proper disruption using a nuclear subsurface explosion with shallow burial is a feasible strategy, providing considerable impact damage reduction if all other approaches fail.