Hydrogels are water-swollen, typically soft networks useful as biomaterials and in other fields of biotechnology. Hydrogel networks capable of sensing and responding to external perturbations, such as light, temperature, pH, or force, are useful across a wide range of applications requiring on-demand cross-linking or dynamic changes. Thus far, although mechanophores have been described as strain-sensitive reactive groups, embedding this type of force-responsiveness into hydrogels is unproven. Here, we synthesized multifunctional polymers that combine a hydrophilic zwitterion with permanently cross-linking alkenes, and dynamically cross-linking disulfides. From these polymers, we created hydrogels that contain irreversible and strong thiol-ene cross-links and reversible disulfide cross-links, and they stiffened in response to strain, increasing hundreds of kPa in modulus under compression. We examined variations in polymer composition and used a constitutive model to determine how to balance the number of thiol-ene vs disulfide cross-links to create maximally force-responsive networks. These strain-stiffening hydrogels represent potential biomaterials that benefit from the mechanoresponsive behavior needed for emerging applications in areas such as tissue engineering.