An attitude dynamics model of spacecraft with variable speed control moment gyroscope (VSCMG), is obtained using the framework of geometric mechanics. This attitude dynamics formulation relaxes some standard assumptions, that are made in the prior literature on control moment gyroscopes and provides a general dynamics model. The dynamics equations show the complex nonlinear coupling between the internal degrees of freedom associated with the VSCMG and the spacecraft base body attitude degrees of freedom. General ideas on how this coupling can be used to control the angular momentum of the base body of the spacecraft using changes in the momentum variables of a finite number of VSCMGs, are provided. A special case of three VSCMGs arranged in tetrahedron configuration is considered. A control scheme using three VSCMG for an attitude pointing maneuver in the absence of external torques and when the total angular momentum of the spacecraft is zero, is presented. Geometric Variational Integrators are constructed for this underactuated system and the control scheme is numerically validated.