The machine comprises a rotary drum (8) provided with a circumferential series of twisting and cutting parts (10, 11, 19) arranged along generatrices of the drum. The twisting parts are composed of pairs of male-female pliers (10, 11) made to translate relatively between an open position and a closed position and with partially telescoping of the same. The cutting parts (19) are composed of sliding knives normally housed in corresponding recesses (23) of one of the pliers (10, 11) and which can be driven to project therefrom to cut the continuous sausage when the pliers (10, 11) are in the closed position.