In this paper, we propose a new dynamic IRS beamforming framework to boost the sum throughput of an intelligent reflecting surface (IRS) aided wireless powered communication network (WPCN). Specifically, the IRS phase-shift vectors across time and resource allocation are jointly optimized to enhance the efficiencies of both downlink wireless power transfer (DL WPT) and uplink wireless information transmission (UL WIT) between a hybrid access point (HAP) and multiple wirelessly powered devices. To this end, we first study three special cases of the dynamic IRS beamforming, namely user-adaptive IRS beamforming, UL-adaptive IRS beamforming, and static IRS beamforming, by characterizing their optimal performance relationships and proposing corresponding algorithms. Interestingly, it is rigorously proved that the latter two cases achieve the same throughput, thus helping halve the number of IRS phase shifts to be optimized and signalling overhead practically required for UL-adaptive IRS beamforming. Then, we propose a general optimization framework for dynamic IRS beamforming, which is applicable for any given number of IRS phase-shift vectors available. Despite of the non-convexity of the general problem with highly coupled optimization variables, we propose two algorithms to solve it and particularly, the low-complexity algorithm exploits the intrinsic structure of the optimal solution as well as the solutions to the cases with user-adaptive and static IRS beamforming. Simulation results validate our theoretical findings, illustrate the practical significance of IRS with dynamic beamforming for spectral and energy efficient WPCNs, and demonstrate the effectiveness of our proposed designs over various benchmark schemes.