Co atoms and dimers embedded in a Cu(110)(2 × 1)-O surface oxide are investigated via low-temperature STM/STS experiments and first-principles simulations. It is found that Co dimers incorporated into adjacent rows of the Cu(110)(2 × 1)-O reconstruction show Kondo resonances decoupled from each other, whereas they are antiferromagnetically coupled (and do not exhibit a Kondo effect) when they are aligned on the same row. This shows that it is possible to decouple single carriers of the Kondo effect via a proper choice of the adsorption and host geometry. It is also shown that an oxidic environment presents features remarkably different from those of pure metal substrates.