A cutting unit for cutting a strip of packing material; the cutting unit comprising: at least one blade (11; 9); a supporting body having a seat for housing the blade (11; 9); and at least one adjusting member, which is inserted in a slide channel formed in the supporting body so as to slide axially along the slide channel, and is coupled mechanically to the blade (11; 9) housed inside the seat to adjust the position of the blade (11; 9) according to its own axial position along the slide channel; wherein the supporting body is divided into a movable portion in which the seat housing the blade (11; 9) is formed and a fixed portion adjacent to the movable portion; wherein the supporting body comprises at least one first cut separating the movable portion from the fixed portion; wherein the movable portion of the supporting body is movable elastically with respect to the fixed portion by elastic deformation of the supporting body itself; wherein by sliding axially along the slide channel, the adjusting member generates a variable thrust between the movable portion of the supporting body and the fixed portion of the supporting body that moves the movable portion away from the fixed portion starting from a neutral state without elastic deformations of the supporting body and consequently determining an elastic deformation of the supporting body; and wherein by remaining still along the slide channel, the adjusting member maintains the movable portion of the supporting body at a given and constant distance from the fixed portion of the supporting body thus preventing the movable portion to move close to the fixed portion; the cutting unit being characterized in that, to allow to insert and remove the blade in/from the seat, at the seat, the supporting body comprises at least one second cut, which terminates at the seat and generates a localized weakening of the supporting body to allow an elastic deformation of the seat. at least one blade (11; 9); a supporting body having a seat for housing the blade (11; 9); and at least one adjusting member, which is inserted in a slide channel formed in the supporting body so as to slide axially along the slide channel, and is coupled mechanically to the blade (11; 9) housed inside the seat to adjust the position of the blade (11; 9) according to its own axial position along the slide channel; wherein the supporting body is divided into a movable portion in which the seat housing the blade (11; 9) is formed and a fixed portion adjacent to the movable portion; wherein the supporting body comprises at least one first cut separating the movable portion from the fixed portion; wherein the movable portion of the supporting body is movable elastically with respect to the fixed portion by elastic deformation of the supporting body itself; wherein by sliding axially along the slide channel, the adjusting member generates a variable thrust between the movable portion of the supporting body and the fixed portion of the supporting body that moves the movable portion away from the fixed portion starting from a neutral state without elastic deformations of the supporting body and consequently determining an elastic deformation of the supporting body; and wherein by remaining still along the slide channel, the adjusting member maintains the movable portion of the supporting body at a given and constant distance from the fixed portion of the supporting body thus preventing the movable portion to move close to the fixed portion; the cutting unit being characterized in that, to allow to insert and remove the blade in/from the seat, at the seat, the supporting body comprises at least one second cut, which terminates at the seat and generates a localized weakening of the supporting body to allow an elastic deformation of the seat.