A fluid discharge pumping apparatus includes: a drive mechanism; a cylinder; an outflow valve mechanism and an inflow valve mechanism coupled to the cylinder; a piston member inside the cylinder; and a piston-supporting member attached to the piston member driven by the drive mechanism to move the piston member. The inflow valve mechanism opens when the interior of the cylinder is depressurized, whereas the outflow valve mechanism opens when the interior of the cylinder is pressurized.