SC-GS is a novel representation technique that utilizes sparse control points and dense Gaussian functions to represent the motion and appearance of dynamic scenes, respectively. It learns a compact 6-degree-of-freedom (6DOF) transformation basis using a small number of control points, which can be locally interpolated through weight interpolation to obtain a motion field for the 3D Gaussian function. By employing a deformation MLP to predict the time-varying 6DOF transformation for each control point, the method reduces the complexity of learning and enhances its capacity, achieving coherent spatiotemporal motion patterns. Simultaneously, it conjointly learns the 3D Gaussian function, the canonical space positions of the control points, and the deformation MLP to reconstruct the 3D scene's appearance, geometry, and dynamics. During training, the position and number of control points are adaptively adjusted to suit the motion complexity of different regions. A constraint loss function that enforces spatial continuity and local rigidity is also adopted. Thanks to the explicit sparsity of the motion representation and the separation of appearance, this method enables user-controlled motion editing while preserving high-fidelity appearance. Extensive experiments demonstrate that the proposed method outperforms existing approaches in new view synthesis and high-speed rendering, and supports novel applications of user-controlled motion editing with preserved appearance.