A time-dependent initial value semiclassical propagator is developed and applied to dissociation dynamics. Numerically implementable formulas are given for computing detailed dissociation dynamics and photofragmentation matrix elements. The method is applied to the study of two- and three-dimensional HOH/HOD photodissociation in the (A) over tilde state. In the two-dimensional case, results obtained by a grid-based numerical integration method using relatively few classical trajectories show very good agreement with known quantum results. The three-dimensional study uses a stationary-phase Monte Carlo approach to computing dissociation cross sections. In this case a comparison with exact quantum calculations shows only qualitative agreement.