Atomic-scale simulations are performed to study the vertical manipulation of single Co adatoms on a Cu(001) surface using a scanning tunneling microscopy (STM) tip. Cu and Co tips with different geometries are investigated. Our results demonstrate that the details of the tip significantly affect the manipulation of the Co adatom. The differences in the manipulation of the Co adatom using different tips and the dependence on tip geometry are revealed. The possibilities and mechanism of extracting single adatoms on metal surfaces with a STM tip at zero bias voltage are explored.