Smart materials with self-growing and tailorable mechanical strength have wide-range potential applications in self-healing, self-repairing, self-assembly, artificial muscle, soft robots and intelligent devices. However, their working mechanisms and principles are not fully understood yet and mathematically and physical modeling is a huge challenge, as traditionally synthesized materials cannot self-grow and reconstruct themselves once formed or deformed. In this study, a phenomenological constitutive model was developed to investigate the working mechanisms of self-growing and tailorable mechanical strength in double-network (DN) hydrogel composites, induced by mechanochemical transduction of dynamic-modal mechanophore. An extended Maxwell model was firstly employed to characterize the mechanical unzipping of hydrogel composites, and then mechanochemically induced destruction and reconstruction processes of brittle network in the hydrogel composite were formulated. The enhanced mechanical strength of brittle network has been identified as the key driving force to generate self-growing and tailorable mechanical strength in the hydrogel composite. Finally, a stress-strain constitutive relationship was developed for the dynamic-modal mechanophore in the hydrogel composite. Simulation results obtained from the proposed model were compared with the experimental data, and a good agreement has been achieved. This study provides an effective strategy for modelling and exploring the working mechanism in the mechanoresponsive DN hydrogel composites with self-growing and tailorable mechanical strength.