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 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 } _ { \odot }  around \sim  1 { M } _ { \odot }  stars survive for \sim  4 \times 10 ^ { 6 } years , assuming a viscosity parameter \alpha = 0.01 , a time-dependent FUV luminosity L _ { FUV } \sim 10 ^ { -2 } -10 ^ { -3 } { L } _ { \odot }  and with X-ray and EUV luminosities L _ { X } \sim L _ { EUV } \sim 10 ^ { -3 } L _ { \odot } . We find that FUV/X-ray-induced photoevaporation and viscous accretion are both important in depleting disk mass . Photoevaporation rates are most significant at \sim  1-10 AU and at \gtrsim  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 ( \sim 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 } _ { * }  \lesssim  3 { M } _ { \odot } ; for { M } _ { * }  \gtrsim  3 { M } _ { \odot }  the disks are short-lived ( \sim 10 ^ { 5 } years ) .