We report the fabrication of a novel epitaxial graphene(EG)/Mn/SiC(0001) sandwiched structure through the intercalation of as-deposited Mn atoms on graphene surfaces, with the aid of scanning tunneling microscope, low energy electron diffraction, and X-ray photoelectron spectroscopy. We found that Mn can intercalate below both sp(3)-hybridized carbon-rich interface layer and monolayer graphene, along with the formation of various embedded Mn islands showing different surface morphologies. The unique trait of the sandwiched system is that the strong interaction between the carbon-rich interface layer and SiC(0001) can be decoupled to some degrees, and contemporaneous, an n-doping effect is observed by mapping the energy band of the system using angle-resolved photoemission spectroscopy. Moreover, what deserves our special attention is that the intercalated islands can only evolve below monolayer graphene when a bilayer coexists, accounting for an intriguing graphene thickness-dependent intercalation effect. In the long run, we believe that the construction of graphene/Mn/SiC(0001) systems offers ideal candidates for exploring some intriguing physical properties such as the magnetic property of two-dimensional transition metal systems.