This manuscript presents the formulation and implementation of a particle-resolved 3D finite element (3DFE) model to study the effect of cathode microstructure on the electrochemical and mechanical responses of lithium-ion batteries (LIBs) during the discharge process. In this model, active particles (lithium iron phosphate) are explicitly resolved to allow the direct assignment of boundary conditions on particle surfaces. To incorporate the effect of binder phase in a numerically efficient manner, it is modeled as a homogenized matrix with a pore-filling electrolyte that allows the transport of both electrons and ions. A new virtual packing algorithm is implemented to reconstruct three cathode microstructures, one of which has an idealized microstructure with spherical particles of similar radii. This microstructural model is used for the verification of the 3DFE model through comparison with the pseudo two-dimensional (P2D) model. The other two cathodes, which are composed of two-size spherical and arbitrary-shaped particles, are used to study the impact of microstructure and discharge rate on the electro-chemo-mechanical behavior. The proposed model predicts the effect of electrode microstructure on active material utilization, as well as the magnitude and distribution of mechanical stresses developed in particles. We also study how the mechanical response of the cathode is affected by the binder stiffness.