An apparatus for cutting off and joining a sheet element to a container includes an operating unit including a cutting device with a cutting edge surrounding a joining device. The operating unit and the container are movable with respect to one another along a movement axis between a spaced condition, in which a sheet material is interposed therebetween and is spaced therefrom, and a joined condition, in which the joining device joins the material to the container. A retaining device retains the material during joining and cutting. In the joined condition, the cutting device remains fixed relative to the joining device and the retaining device moves along the axis from tensioning to cutting positions, the sheet element being cut on the cutting edge from the material during movement of the retaining device from the tensioning to the cutting positions.