We investigate the role of substrates on the collective excitations of graphene by using a first-principles implementation of the density response function within the random-phase approximation. Specifically, we consider graphene adsorbed on SiC(0001) and Al(111) as representative examples of a semiconducting and metallic substrate. On SiC(0001), the long wavelength π plasmons are significantly damped although their energies remain almost unaltered. On Al(111), the long wavelength π plasmons are completely quenched due to the coupling to the metal surface plasmon. The strong damping of the plasmon excitations occurs despite the fact that the single-particle band structure of graphene is completely unaffected by the substrates illustrating the nonlocal nature of the effect.