When hydrogels are designed for biological applications, the mechanical properties are carefully chosen to match their precise application. However, traditional methodologies of mechanical characterization (simple shear or compression/extension) commonly ignore the multiaxiality of in vivo deformations. A recent study highlights that biopolymers and tissue indeed show a complex response to combined uniaxial and shear strains. In this study a synthetic yet biomimetic fibrous hydrogel is used, which is based on polyisocyanides and forms a self‐assembled network of branched semiflexible chains, similar in architecture networks of structural biopolymers like actin, collagen, and fibrin. Its synthetic nature allows to decouple key parameters of these networks and individually understand their impact on the mechanical response under multiaxial deformation. Experimentally, it is found that the persistence length is a key parameter of biological networks, which tunes softening of gels under compression: The stiffer the polymer, the more the network softens in compression. This study provides insights into tissue behavior that likely is only obtainable from synthetic model systems and is able to direct further the design of new synthetic biomimetic soft materials that are in high demand as tunable bio‐free extracellular matrix materials.