We present the mixed Galerkin discretization of distributed-parameter port-Hamiltonian systems. Due to the inherent definition of (boundary) interconnection ports, this system representation is particularly useful for the modeling of interconnected multi-physics systems and control. At the prototypical example of a system of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure, (ii) its geometric approximation by a finite-dimensional Dirac structure using a mixed Galerkin approach and power-preserving maps on the space of discrete power variables and (iii) the approximation of the Hamiltonian to obtain finite-dimensional port-Hamiltonian state space models. The power-preserving maps on the discrete bond space offer design degrees of freedom for the discretization, which is illustrated at the example Whitney finite elements on a 2D simplicial triangulation. The resulting schemes can be considered as trade-offs between centered approximations and upwinding.