We have found that tungsten (W) foils can be used for controlling the carbon diffusion within copper (Cu) enclosures to synthesize large-domain bi-/multi-layer-free monolayer graphene via chemical vapor deposition. We have observed that bi-/multi-layer graphene that nucleate underneath the monolayer graphene can be selectively removed by a W foil placed inside of the Cu enclosure. Both X-ray photoelectron spectroscopy and X-ray diffraction reveal the formation of tungsten sub-carbide (W2C), suggesting the role of the W foil as a carbon sink that alters the carbon concentration inside of the enclosure. Consequently, the bi-/multi-layers appear to dissolve. Utilizing this selective removal process, we were able to demonstrate large-domain (>200 μm) monolayer graphene that is free of any bi-/multi-layers by using Cu double enclosures.