We present the time evolution of viscously accreting circumstellar disks as they are irradiated by ultraviolet and X-ray photons from a low-mass central star. Our model is a hybrid of a one-dimensional (1D) time-dependent viscous disk model coupled to a 1+1D disk vertical structure model used for calculating the disk structure and photoevaporation rates. We find that disks of initial mass 0.1 M _☉ around ~1 M _☉ stars survive for ~4 × 10⁶ yr, assuming a viscosity parameter α = 0.01, a time-dependent FUV luminosity L _FUV ~ 10^–2-10^–3 L _☉ and with X-ray and EUV luminosities L_X ~ L _EUV ~ 10^–3 L _☉. We find that FUV/X-ray-induced photoevaporation and viscous accretion are both important in depleting disk mass. Photoevaporation rates are most significant at ~1-10 AU and at 30 AU. Viscosity spreads the disk which causes mass loss by accretion onto the central star and feeds mass loss by photoevaporation in the outer disk. We find that FUV photons can create gaps in the inner, planet-forming regions of the disk (~1-10 AU) at relatively early epochs in disk evolution while disk masses are still substantial. EUV and X-ray photons are also capable of driving gaps, but EUV can only do so at late, low accretion-rate epochs after the disk mass has already declined substantially. Disks around stars with predominantly soft X-ray fields experience enhanced photoevaporative mass loss. We follow disk evolution around stars of different masses, and find that disk survival time is relatively independent of mass for stars with M _* 3 M _☉; for M _* 3 M _☉ the disks are short-lived (~10⁵ yr).