A method and apparatus for cutting a paper web (W) in a group of drying cylinders provided with single-wire draw (13) in a paper machine or a finishing machine. The drying wire (13) is separated from the paper web (W) by one or more guide rolls (14a, 14b) thereby creating a open draw (W.sub.0) for the web (W). The cutting of the paper web (W) is carried out at the open draw (W.sub.0) of the web (W). After the open draw (W.sub.0), the drying wire (13) and the web (W) are rejoined on the surface of the following leading or drying cylinder (11). Preferably, two guide rolls (14a, 14b) are utilized whereby the first roll is disposed so that the drying wire (13) supports the web (W) up to the location of the guide roll (14a), which is followed by an open draw (W.sub.0) of the web. The drying wire (13) is returned onto the following leading or drying cylinder (11) with the second guide roll (14b).