Mechanical interactions between cells and their 3D environment govern fundamental processes in tissue development, cancer, and regeneration. Yet, it is challenging to modulate the mechanical cues that cells experience, thus limiting the ability to study these processes in vitro. Natural tissue microenvironments display complex viscoelastic behaviors and undergo continuous remodeling—properties not easily reproduced in synthetic cell culture matrices. Here, principles of DNA nanotechnology are leveraged to introduce programmable mechanical cues into a hydrogel that guides and interrogates the development of embedded cells. By systematically modulating stiffness and stress relaxation, two distinct timescales of mechano-sensitive processes controlling polarity in epithelial cells are uncovered. Our analysis highlights that the commonly reported matrix “stiffness” value, often measured at ≈ 1 Hz frequency, has limited physiological relevance. These findings prompted us to develop novel switchable DNA modules that enable dynamic viscoelasticity changes during ongoing cell culture. The controlled matrix reconfiguration induces reversible cell polarity inversions and guides the morphogenesis of complex multicellular structures. The material platform offers unprecedented control over the mechanical microenvironment, opening new avenues for advanced applications in biophysics, tissue engineering, and disease modeling.