An apparatus for slitting a sheet material web as it is wound onto a roll including at least one winding drum supporting the web, a moveably reel spool positioned in a parallel and spaced apart relationship with the winding drum, a slitting device and a control system. The slitting device includes a track member and a slitting member moveably mounted on the track member. The slitting member continuously slits the sheet material web longitudinally along its length as it is wound onto the roll. The control system controls the position of the slitting member on the track so as to maintain a predetermined penetration of the slitting member within the roll as the roll increases in size. A method for continuously slitting the roll includes carrying the sheet material web over a winding drum, depositing the sheet material web onto a rotating reel spool to form a roll of sheet material web, moving the slitting member so as to continuously slit the sheet material web on the roll and controlling the movement of the slitting member with a control system so as to maintain a predetermined depth of penetration of the slitting member within the roll.