Device for locking two adjacent sections (1, 2) of a roll of paper (3) placed on the sides of a cutting section plane (4) defined by the movement of a cutting blade (5) of a cutting-off machine (M), comprising a pair of clamping devices (6, 7) configured to be able to assume an unlocking configuration with a locking configuration of respective sections (1, 2) of the roll (3); at least a first actuator (8) which can be operated on command to pass said clamping devices from the unlocking configuration to the locking configuration of the respective sections (1, 2), and vice versa; at least a second actuator (10) connected to the clamping devices (6, 7) and configured to perform a movement of reciprocal distancing of the clamping devices in a locking configuration with respect to said cutting section plane (4); means of inhibition (11) of the reciprocal moving away of the clamping devices active during the cutting advancement of the blade (5) through the roll (3); and activation means (12) of the second actuator (10) of the clamping devices (6, 7) configured to activate the reciprocal removal of the clamping devices immediately after the end of the roll cutting phase (3) performed by the blade (5).