Due to the imaging limitation of depth sensors, high-resolution (HR) depth maps are often difficult to be acquired directly, thus effective depth super-resolution (DSR) algorithms are needed to generate HR output from its low-resolution (LR) counterpart. Previous methods treat all depth regions equally without considering different extents of degradation at region-level, and regard DSR under different scales as independent tasks without considering the modeling of different scales, which impede further performance improvement and practical use of DSR. To alleviate these problems, we propose a deep controllable slicing network from a novel perspective. Specifically, our model is to learn a set of slicing branches in a divide-and-conquer manner, parameterized by a distance-aware weighting scheme to adaptively aggregate different depths in an ensemble. Each branch that specifies a depth slice (e.g., the region in some depth range) tends to yield accurate depth recovery. Meanwhile, a scale-controllable module that extracts depth features under different scales is proposed and inserted into the front of slicing network, and enables finely-grained control of the depth restoration results of slicing network with a scale hyper-parameter. Extensive experiments on synthetic and real-world benchmark datasets demonstrate that our method achieves superior performance. CCS CONCEPTS • Computing methodologies → 3D imaging; Reconstruction.