A piston pump device has a support unit, a pump cylinder, and a pump piston arranged in the pump cylinder. The pump cylinder has a longitudinal center axis, and a cylinder bottom arranged perpendicular to the longitudinal center axis. The pump piston is movable relative to the cylinder bottom, and the pump cylinder is secured on the support unit by a securing unit. The securing unit has a leaf spring, which permits a pivoting movement of the longitudinal center axis of the pump cylinder relative to the support unit. The piston pump device is wear-resistant and runs quietly. When used as a suction pump, the piston pump device additionally permits a controllable air flow until the pump comes to a stop.