3D soft bioscaffolds have great promise in tissue engineering, biohybrid robotics, and organ-on-a-chip engineering applications. Though emerging three-dimensional (3D) printing techniques offer versatility for assembling soft biomaterials, challenges persist in overcoming the deformation or collapse of delicate 3D structures during fabrication, especially for overhanging or thin features. This study introduces a magnet-assisted fabrication strategy that uses a magnetic field to trigger shape morphing and provide remote temporary support, enabling the straightforward creation of soft bioscaffolds with overhangs and thin-walled structures in 3D. We demonstrate the versatility and effectiveness of our strategy through the fabrication of bioscaffolds that replicate the complex 3D topology of branching vascular systems. Furthermore, we engineered hydrogel-based bioscaffolds to support biohybrid soft actuators capable of walking motion triggered by cardiomyocytes. This approach opens new possibilities for shaping hydrogel materials into complex 3D morphologies, which will further empower a broad range of biomedical applications.