Recently, there is great interest in considering the energy efficiency aspect of cellular networks. On the other hand, the power grid infrastructure, which provides electricity to cellular networks, is experiencing a significant shift from the traditional electricity grid to the smart grid. When a cellular network is powered by the smart grid, only considering energy efficiency in the cellular network may not be enough. In this paper, we consider not only energy-efficient communications but also the dynamics of the smart grid in designing green wireless cellular networks. Specifically, the dynamic operation of cellular base stations depends on the traffic, real-time electricity price, and the pollutant level associated with electricity generation. Coordinated multipoint (CoMP) is used to ensure acceptable service quality in the cells whose base stations have been shut down. The active base stations decide on which retailers to procure electricity from and how much electricity to procure. We formulate the system as a Stackelberg game, which has two levels: a cellular network level and a smart grid level. Simulation results show that the smart grid has significant impacts on green wireless cellular networks, and our proposed scheme can significantly reduce operational expenditure and CO_2 emissions in green wireless cellular networks.