A321 Pilot reported a tug driver pushed them back into the wrong direction to the wrong spot twice.

Narrative

Ramp Control gave clearance 'push approved; tail south; drop point zulu'. First Officer (FO) read back clearance; stated clearance to me and I stated the exact clearance to the tug driver. The tug driver started the push; cleared us to start engines and then proceeded to push tail east toward spot/line XX. As we were eyes down monitoring the engine start; the ramp call us to 'halt the push' and queried as to what we were doing. I then explained to the tug driver his error; talk his eyes to point zulu and gave specific instructions to push tail south; drop zulu which is toward Gate X. The tug driver stated he understood and then began pushing us toward spot/line XY. At this point Ramp Control directed that we pull back to the gate. Simultaneously a Crew Chief ran onto the ramp; took control of the tug; made communications contact with me at which point I directed him to pull us back to Gate Y. Upon arrival at Gate Y we request the jet bridge be attached; we performed the engine shutdown checklist; and departed the aircraft.A tug driver who is either improperly trained or unqualified being allowed to push the aircraft. Not knowing the qualification levels of the ground crew; I have no input due to lack of information.