By performing ab initio calculations, we reveal an unexpected behavior of the exchange interactions between the Fe STM tip and the Fe adatom on Cu(001) and on a Cu₂N monolayer on Cu(001) surfaces [denoted as Cu₂N/Cu(001)]. A tip-adatom distance-dependent antiferromagnetic-ferromagnetic transition and antiferromagnetic exchange interactions between the tip and the adatom are found for these two junctions, respectively. We demonstrate that the different exchange interactions in these systems are determined by the competition between the tip-adatom and the adatom-substrate interactions. Based on transport calculations, we found that the spin polarization and magnetoresistance in the junction on the Cu(001) system and on the Cu₂N/Cu(001) system depend on the tip-adatom distance.