The propagation of waterflood-induced fractures (WIFs) occurs during prolonged water injection and is influenced by the distribution and properties of natural fractures (NFs). Available numerical models rarely consider fracture activation and rupture in an integrated manner, which makes it difficult to reflect complex fracture morphology. In this paper, we propose a hydraulic-mechanical model with strain-dependent damage variables to describe the dynamic expansion characteristics of WIFs. There are discrete filled NFs in the matrix with non-equal-thickness joint elements, for which we derive the constitutive equations to calculate fracture widths during water injection and production. Damage variables for the matrix and fractures are calculated according to the maximum tensile stress criterion and the Mohr–Coulomb criterion. A comparison between the coupled model and experimental results is conducted to demonstrate its validity. Finally, we simulated and analyzed four influencing factors of the pressure response and fracture evolution. The study demonstrates that fracture behavior and damage area evolution are highly sensitive to injection rate, communication sequence, NF density, and orientation. The activation, cross, and capture interactions between NFs and WIFs complicate the fracture-damage network and enhance seepage efficiency. High injection rates promote crack tip propagation, while lower rates facilitate the evolution of secondary fractures at low pressure. For high NF density reservoirs, low-pressure injection fully activates NFs, aiding damage evolution. In low NF density reservoirs, excessive pressure induces simpler fracture morphologies, making unstable water injection more effective than continuous injection. This work guides appropriately induced fractures to improve water absorption in tight reservoirs.