We investigate viscous fluid flows and concurrent fluid-driven deformations in porous media. The hydro-mechanically (H-M) coupled pore-network model (PNM) is developed, which combines the two-dimensional square-lattice PNM and block-spring model. The single-/two-phase flows into saturated deformable porous media are simulated through iterative two-way coupling method in H-M coupled PNM. A comparison between simulations and laboratory observations on flow patterns, solid deformation behaviors, and pressure responses ensures the validity of our H-M coupled PNM in both single-/two-phase flows. Parametric studies using the validated model examine the effects of mechanical coupling, stiffness of solid particles, the viscosity of invading fluids, injection flow rate, and degree of disorder during immiscible viscous fluid injection. The viscous fluid-driven deformation increases the pore throat size and hence reduces the injection pressure. In particular, the viscosity of invading fluid significantly alters the patterns of fluid propagation and solid deformation, along with a transition from the viscous fingering to the stable displacement with increasing viscosity. Moreover, the structural disorder in porous networks magnifies the irregular flow pattern, the pressure fluctuation associated with Haines jumps, and the poromechanical deformation. The particle-level force analysis delineates two distinct regimes: fluid invasion with no deformation and drag-driven deformation, which depends on the balance between the seepage drag force and the skeletal force. The presented results contribute to a better understanding of the H-M coupled fluid flows during the injection of viscous fluids into disordered-deformable porous media.