One of the most intriguing and important aspects of biological supramolecular materials is its ability to adapt macroscopic properties in response to environmental cues for controlling cellular processes. Recently, bulk matrix stiffness, in particular, stress sensitivity, has been established as a key mechanical cue in cellular function and development. However, stress-stiffening capacity and the ability to control and exploit this key characteristic is relatively new to the field of biomimetic materials. In this work, DNA-responsive hydrogels, composed of semiflexible PIC polymers equipped with DNA cross-linkers, were engineered to create mimics of natural biopolymer networks that capture these essential elastic properties and can be controlled by external stimuli. We show that the elastic properties are governed by the molecular structure of the cross-linker, which can be readily varied providing access to a broad range of highly tunable soft hydrogels with diverse stress-stiffening regimes. By using cross-linkers based on DNA nanoswitches, responsive to pH or ligands, internal control elements of mechanical properties are implemented that allow for dynamic control of elastic properties with high specificity. The work broadens the current knowledge necessary for the development of user defined biomimetic materials with stress stiffening capacity.