The carbon and water cycles in the Earth’s interior are linked to key planetary processes, such as mantle melting, degassing, chemical differentiation, and advection. However, the role of water in the carbon exchange between the mantle and core is not well known. Here, we show experimental results of a reaction between Fe₃C and H₂O at pressures and temperatures of the deep mantle and core-mantle boundary (CMB). The reaction produces diamond, FeO, and FeH_x, suggesting that water can liberate carbon from the core in the form of diamond (“core carbon extraction”) while the core gains hydrogen, if subducted water reaches to the CMB. Therefore, Earth’s deep water and carbon cycles can be linked. The extracted core carbon can explain a significant amount of the present-day mantle carbon. Also, if diamond can be collected by mantle flow in the region, it can result in unusually high seismic-velocity structures.