Gate-controlled electron trap dynamics are quantitatively investigated to elucidate their influence on the spectral and temporal characteristics in MoS2-WSe2 heterostructure photodetector. Defect-induced trap states within the bandgap enable sub-bandgap photon absorption, thereby extending the photodetection range up to 1650 nm. As the gate voltage increases, the Fermi level shifts toward the conduction band, which raises the probability of electron trap occupation and consequently suppresses absorption in certain wavelength ranges. Moreover, increased trap occupancy significantly shortens the photocurrent rising time from 480 ms at -40 V to 1.3 ms at +40 V, whereas the falling time becomes longer because of the reduced trap-assisted recombination. These results indicate that both spectral responsivity and photoresponse time can be dynamically modulated by the gate bias, allowing the device to function as a tunable photodetector that adapts its detection mode to specific application requirements. This study provides fundamental insight into trap-assisted photodetection mechanisms and establishes a platform for future research on gate-controlled optoelectronic devices.