The electron dynamics in a TiO2/alizarin based dye-sensitized solar cell is studied by a means of ab initio nonadiabatic molecular dynamics. The effects of surface terminations and vacancy defects on photoexcited interfacial electron transfer (ET) and energy relaxation of injected electrons are examined in detail. In particular, we consider three plausible TiO2 surface terminations which are stable at zero temperature. However, only one of them maintains structural integrity at room temperature while the other two terminations lead to broken interfacial Ti-O bonds. An ultrafast ET dynamics (4.6 fs) is observed for the intact interface, consistent with relevant experimental and theoretical results. On the other hand, the ET dynamics of the two other terminations takes either a much longer time or results in less charge transfer. The surface vacancies in TiO2 are found to play important roles in the structural integrity, the interfacial ET dynamics, and the energy relaxation in the TiO2 conduction bands. For example, O vacancies are observed to enhance the interfacial bonding, delocalize the photoexcited state, and facilitate nonadiabatic ET. On the other hand, Ti vacancies give rise to less stable interfacial structure and negligible ET. The energy relaxation time scale for the injected electron in the conduction band is 500 fs regardless of the vacancies. Both O and Ti surface vacancies are found to trap the injected electron while the O vacancies could increase the charge recombination at the interface.