We propose VoxMorph, a new interactive freeform deformation tool for high-resolution voxel grids. Our system exploits cages for high-level deformation control. We tackle the scalability issue by introducing a new 3-scale deformation algorithm composed of a high quality as-rigid-as possible deformation at coarse scale, a quasi-conformal space deformation at mid-scale and a new deformation-adaptive local linear technique at fine scale. The two first scales are applied interactively on a visualization envelope, while the complete full resolution deformation is computed as a post-process after the interactive session, resulting in a high-resolution voxel grid containing the deformed model. We tested our system on various real world datasets and demonstrate that our approach offers a good balance between performance and quality.