A method of cutting out an opening in a flat cardboard blank (10, 12) for manufacturing a package, the blank having a first face and an opposite second face, the method comprising: - forming a closed-loop cutout line in the cardboard blank (10, 12), the cutout line defining a first portion of the blank (10, 12) and a second portion of the blank (10, 12) outside the cutout line; - bringing the first face of the blank (10, 12) to face an ejector tape including an adhesive layer, the ejector tape being arranged with its adhesive layer on a side towards the first face of the blank (10, 12) and facing the first portion of the blank (10, 12); - bringing the blank (10, 12), with its cutout line, and the ejector tape to face each other between a presser tool and an activation tool that face each other; - the activation tool presenting a protruding active face facing towards the ejector tape and the blank (10, 12), with its protruding portion being defined by a peripheral edge; - a projection of the peripheral edge perpendicularly onto a plane in which the blank (10, 12) extends being inscribed inside the cutout line with an activation radial margin towards the inside away from the cutout line; - inside the peripheral edge, the active face presenting a recess; - the presser tool presenting a boss projecting towards the blank (10, 12) from a peripheral surface facing towards the blank (10, 12), the boss presenting an outline relative to the peripheral surface; - a projection of the outline of the boss perpendicularly onto the plane in which the blank (10, 12) extends being inscribed inside the projection of the peripheral edge of the activation tool perpendicularly onto said plane with a pressing radial margin towards the inside; and - pressing together the first portion of the blank (10, 12) and the facing ejector tape between the presser tool and the facing activation tool in such a manner as to cause the ejector tape to stick exclusively to the first portion of the blank (10, 12). - and in that, after having pressed together the first portion of the blank (10,12) and the facing ejector tape between the presser tool and the facing activation tool, the ejector tape is separated from the second portion of the blank, the first portion being separated from the second portion of the blank by being stuck to the facing ejector tape. - forming a closed-loop cutout line in the cardboard blank (10, 12), the cutout line defining a first portion of the blank (10, 12) and a second portion of the blank (10, 12) outside the cutout line; - bringing the first face of the blank (10, 12) to face an ejector tape including an adhesive layer, the ejector tape being arranged with its adhesive layer on a side towards the first face of the blank (10, 12) and facing the first portion of the blank (10, 12); - bringing the blank (10, 12), with its cutout line, and the ejector tape to face each other between a presser tool and an activation tool that face each other; - the activation tool presenting a protruding active face facing towards the ejector tape and the blank (10, 12), with its protruding portion being defined by a peripheral edge; - a projection of the peripheral edge perpendicularly onto a plane in which the blank (10, 12) extends being inscribed inside the cutout line with an activation radial margin towards the inside away from the cutout line; - inside the peripheral edge, the active face presenting a recess; - the presser tool presenting a boss projecting towards the blank (10, 12) from a peripheral surface facing towards the blank (10, 12), the boss presenting an outline relative to the peripheral surface; - a projection of the outline of the boss perpendicularly onto the plane in which the blank (10, 12) extends being inscribed inside the projection of the peripheral edge of the activation tool perpendicularly onto said plane with a pressing radial margin towards the inside; and - pressing together the first portion of the blank (10, 12) and the facing ejector tape between the presser tool and the facing activation tool in such a manner as to cause the ejector tape to stick exclusively to the first portion of the blank (10, 12). - and in that, after having pressed together the first portion of the blank (10,12) and the facing ejector tape between the presser tool and the facing activation tool, the ejector tape is separated from the second portion of the blank, the first portion being separated from the second portion of the blank by being stuck to the facing ejector tape.