During tunnel blasting excavation in soft rock formations, the dynamic response and time-dependent behavior of the surrounding rock are critical to construction stability and long-term safety. However, existing research has insufficiently addressed the damage evolution mechanism of soft rock under the coupled effects of transient blasting loads and long-term creep. This study, based on a mountain tunnel in Hunan Province, employs a combination of theoretical analysis, numerical simulation, and parameter inversion to systematically investigate the dynamic response process of soft rock tunnels under blasting. The main findings are as follows: (1) The established fractional-order creep-damage constitutive model effectively simulates the dynamic response under blasting, with numerical results closely matching indoor model tests and deformation prediction errors below 5%; (2) The strain response of the surrounding rock lags behind the peak blasting stress. Specifically, an instantaneous plastic strain zone forms in the rock mass closest to the tunnel face under blasting loads. The displacements at the tunnel crown and invert exhibit a parabolic decline, while the convergence deformations on the left and right sidewalls are approximately equal. The peak strain in the rock mass occurs after the peak blasting stress. The maximum negative strain (deformation toward the surrounding rock) near the blasting face appears at 6.3 ms, and the maximum positive strain occurs at 16 ms; (3) The intelligent parameter inversion method based on the Particle Swarm Optimization (PSO) algorithm demonstrates high reliability. The optimized values of elastic modulus, Poisson's ratio, and viscosity coefficient obtained through inversion show errors of less than 5% compared to laboratory test results. The coupled constitutive model and intelligent inversion method developed in this study provide an effective theoretical tool for accurately analyzing the dynamic response of soft rock tunnels under blasting. The results can be directly applied to optimize blasting parameters and support design, and offer key technical support for dynamic risk warning and intelligent decision-making during construction.