Interfolding machine of sheet material for making a stack of interfolded sheets (1) equipped with cutting and transferring means, including, for example, a cutting roller 2 that operates the division of the web (10) into sheets (11) of determined length. The cut sheets (11), all having the same length, are carried along the machine up to a transfer roller (3) that transfers them to an “overlap” roller (4). In particular the cutting roller (2) has peripherally a first series of cutting blades (21a)-(21d) arranged at a first angular distance equal to 90° and a second plurality of cutting blades (21′a)-(21′c) arranged at a second angular distance equal to 120°. The length of sheets 11 is therefore achieved by the angular distance existing between the blades (21). In order to adjust the length of the sheets, or cut-off length, one selects the blades on the cutting roller (2) located at an angular distance corresponding to the desired sheet length.