The electronic structure of epitaxial monolayer, bilayer, and trilayer graphene on Ru(0001) was determined by selected-area angle-resolved photoelectron spectroscopy (micro-ARPES). Micro-ARPES band maps provide evidence for a strong electronic coupling between monolayer graphene and the adjacent metal, which causes the complete disruption of the graphene pi-bands near the Fermi energy. However, the perturbation by the metal decreases rapidly with the addition of further graphene sheets, and already an epitaxial graphene bilayer on Ru recovers the characteristic Dirac cones of isolated monolayer graphene. A graphene trilayer on Ru behaves like free-standing bilayer graphene. Density-functional theory based calculations show that this decoupling is due to the efficient passivation of metal d-states by the interfacial graphene layer.