High-Tc superconductors confined to two dimension exhibit novel physical phenomena, such as superconductor-insulator transition. In the Bi2Sr2CaCu2O(8+x) (Bi2212) model system, despite extensive studies, the intrinsic superconducting properties at the thinness limit have been difficult to determine. Here, we report a method to fabricate high quality single-crystal Bi2212 films down to half-unit-cell thickness in the form of graphene/Bi2212 van der Waals heterostructure, in which sharp superconducting transitions are observed. The heterostructure also exhibits a nonlinear current-voltage characteristic due to the Dirac nature of the graphene band structure. More interestingly, although the critical temperature remains essentially the same with reduced thickness of Bi2212, the slope of the normal state T-linear resistivity varies by a factor of 4-5, and the sheet resistance increases by three orders of magnitude, indicating a surprising decoupling of the normal state resistance and superconductivity. The developed technique is versatile, applicable to investigate other two-dimensional (2D) superconducting materials.