The floor heave and the inward movement of sidewalls are often encountered in the excavation of tunnels with swelling rock properties. However, the deformation mechanism for swelling soft-rock tunnels cannot be reasonably revealed even now. In this paper, a time-dependent deformation mechanism is investigated in depth and the viscoelastoplastic deformation is obtained using a nonassociated flow rule and the modified Nishihara model. The continuous degradation behaviors of soft rock induced by the intercoupling between the stressed-dilation and the physicochemical swelling is considered based on the humidity field theory and the Zhang three-dimensional (3D) Hoek-Brown yield criterion. The results show that the time-dependent deformation exhibited is unstable in the secondary creep stage and tends to increase inversely with the values of the Zhang 3D Hoek-Brown criterion parameters and the elastic modulus, while it increases directly with the values of the humidity swelling coefficients and the Poisson’s ratio. The substability creep behavior occurs earlier with decreasing the relaxation time. Furthermore, the sensitivity law of incorporated parameters corresponds well with their corresponding physical meaning and practical significance in this study.