We clarify the dynamics connecting a solar flare and a coronal mass ejection (CME) based on the results of a magnetohydrodynamic (MHD) simulation starting from a nonlinear force-free field (NLFFF) in Inoue et al. 2014. In previous studies, many authors proposed numerous candidates for triggering processes of a solar flare and the associated CME. Among them, the tether-cutting reconnection or the torus instability has been supported by recent simulations and observations. On the other hand, our MHD simulation in accordance with more realistic situations show that highly twisted field lines are first produced through a tether-cutting reconnection between the twisted field lines in the NLFFF, and then the newly formed, strongly twisted field erupts away from the solar surface because of a loss of equilibrium. This dynamics corresponds to the onset of a solar flare. Furthermore we have found that the strongly twisted erupting field reconnect with the weakly twisted ambient field during the eruption, creating a large flux tube, and then it rises over a critical height of the torus instability to trigger a CME. From these results, we conclude that the coupled process of tether-cutting reconnection and torus instability is important in the flare-CME relationship.