The dissociation of a biomolecular complex under the action of periodic and correlated random forcing is studied theoretically. The former is characterized by the period τp and the latter by the correlation time τr. The rupture rates are calculated by overdamped Langevin dynamics and three distinct regimes are identified for both cases by comparison to local relaxation time τR and bond lifetime 〈T〉. For periodic forcing, the adiabatic approximation cannot be applied in the regime τp τR and the bond lifetime is determined by the average pulling. As τR τp 〈T〉, the rupture rate is enhanced by periodic forcing but is τp independent. Analytical expressions are obtained for small and large force amplitudes. As 〈T〉 τp, the rupture rate depends on the phase lag and the process behaves like it is under constant force or loading rate. The result of correlated random forcing is similar to that of periodic forcing. Since the fluctuating forces greater than the average force 〈F〉 contribute more than the fluctuating forces less than 〈F〉, the force fluctuations enhance the rupture rate. As 〈T〉 < τr, the pulling felt by the bond before rupture cannot follow the random forcing protocol and, thus, force fluctuations decline with increasing τr.