Amorphous azopolymers are fascinating materials that can be deformed in arbitrary directions by light. However, they are so far used mostly for microfabrication, to anisotropically reshape dry polymer structures - essentially as a post-processing fabrication step. This is because the effect is known to be a plastic deformation, wherein the azopolymer is photo-softened and selectively reflows along the direction of the illumination polarization, owing to its polarization-dependent functional dyes. Crucially, such deformations are retained in the dark and cannot easily be overwritten by subsequent illumination. Once reflowed, there is no memory of the initial state, and sequential photo-deformations are added on top of each other. Consequently, to use the directional photo-deformation of amorphous azopolymers for dynamic and reconfigurable micro-actuators, e.g., in lab-on-chip applications, one would need to face this lack of overwritability, in addition to a lower deformability of larger structures, sticky behavior, and poor mechanical stability in water for some uses. Here, we show how azopolymer-hydrogel composites overcome these issues. By embedding azopolymer nanoparticles in hydrogel matrices, directional photo-deformation is ensured by the particles, while the compliant gel matrix neatly propagates deformations to the overall composite. Elastic restoring forces from the matrix also promote overwritability, such that microfabricated gel cubes display ample and directionally reconfigurable photo-deformations in water. Sequential illuminations with orthogonal linear polarizations produce alternating linear deformations up to twice the pristine cube side length, using illumination intervals down to five seconds. Finally, we introduce polarization-controlled, fully closeable microwells, with potential applications in biotechnology, microfluidics, and drug release.