Two-dimensional (2D) Janus transition metal dichalcogenides (JTMDs) show direct band gaps and strong visible light absorption with promising applications in photovoltaic cells. Here, we investigate the electronic structures and dynamics of photogenerated carriers in 2D JTMDs and graphene van der Waals sandwich heterojunction (G/JTMDs/G) photovoltaic cells by using first-principles calculations. We find that the intrinsic built-in electric field in JTMDs results in an asymmetry potential, which can be used to effectively enhance the separation and transfer of photogenerated carriers from JTMDs to different graphene layers with a preferred direction within hundreds of femtoseconds in the G/JTMDs/G heterostructures. Furthermore, the photogenerated electrons (holes) can be transferred from monolayer MoSSe (MoSeTe) to the graphene sheets by the Se side with a lower (higher) potential, while the transfer of the photogenerated holes (electrons) is prohibited due to the large separation between the donor and acceptor states.