To study the deformation capacity of tensegrity structures with redundant cables, this paper proposed a method to select the optimal driving mode to achieve structural deformation based on the cable-driven concept with minimal energy dissipation. Firstly, the structural parameters of the tensegrity basic unit and the connection relationship between the member and the node were set, and the mechanical properties analysis was conducted on the structure in the new stable state after the contraction of the cable. This analysis yielded a new calculation formula of the node coordinates. Secondly, the structural parameters and material parameters were assigned to analyze the deformation process of the structure. The passive cables was firstly shrunk to prestress the tensegrity structure, and the additional dissipated elastic potential energy of the structure except for the active cables was calculated. Then, the active cables was shrunk to induce the deformation of the tensegrity structure. The energy dissipation work of the active cables and the final deformation of the structure were calculated. Moreover, the evaluation criteria of the optimal driving mode of the structural deformation were proposed. Finally, taking the double-layer axial splice structure with redundant cables as an example, the active and passive cables of the structure were differentiated and the optimal driving mode was studied. The results show that for the single axial deformation of the structure, when the diagonal cables are active and the middle horizontal cable is passive, the axial change of the structure is maximized while the energy dissipation is minimized. For the composite deformation involving axial deformation and torsional deformation, the composite deformation of the structure is maximized and the energy dissipation is minimized when the diagonal cables opposite to the rod member are active while the remaining diagonal cables are passive.