This paper presents a discrete variational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function.The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems.The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems.This work also extends discrete Noether symmetries to mechanico-electrical dynamical systes.A practical example iS presented to illustrate the results.