The exchange coupling between single 3d magnetic adatoms (Cr, Mn, Fe, and Co) adsorbed on a Cu(001) surface and a Cr STM tip is studied with ab initio calculations. We demonstrate that the spin direction of single adatoms can be controlled by varying the tip-substrate distance, and the sign of the exchange energy is determined by the competition of the direct and the indirect interactions between the tip and the adatom. Based on the spin-dependent transport calculations, we find a magnetoresistance of about 70% at short tip-substrate distances.