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A leading theory for the initiation of coronal mass ejections (CMEs) is the breakout model, in which magnetic reconnection above a filament channel is responsible for disrupting the coronal magnetic field. We present the first simulations of the complete breakout process including the initiation, the plasmoid formation and ejection, and the eventual relaxation of the coronal field to a more potential state. These simulations were performed using a new numerical code that solves the numerical cavitation problems that prevented previous simulations from calculating a complete ejection. Furthermore, the position of the outer boundary in the new simulations is increased out to 30 R☉, which enables determination of the full structure and dynamics of the ejected plasmoid. Our results show that the ejection occurs at a speed on the order of the coronal Alfvén speed and hence that the breakout model can produce fast CMEs. Another key result is that the ejection speed is not sensitive to the refinement level of the grid used in the calculations, which implies that, at least for the numerical resistivity of these simulations, the speed is not sensitive to the Lundquist number. We also calculate, in detail, the helicity of the system and show that the helicity is well conserved during the breakout process. Most of the helicity is ejected from the Sun with the escaping plasmoid, but a significant fraction (of order 10%) remains in the corona. The implications of these results for observation and prediction of CMEs and eruptive flares is discussed.