A closing device arranged above a pierceable point of a closed container including a lower part with a cylindrical discharge nozzle, a screw cover and a piercing element. The piercing element, which is open on both sides, is displaced downwards in an axial direction in a screw-like manner in a screw cover in the lower part of the closing device. The piercing element has two cutting elements offset at an angle which produce a continuous, interconnected cutting line, and a displacing element which shifts a partially cut-out tab of the container from a region of the discharge nozzle.