Tyre-removal apparatus comprising a base having a support for receiving and rotating the wheel. The tyre-removal apparatus further comprising a frame which is joined to the base and which has an upright with a longitudinal axis substantially parallel to an axis of rotation of the wheel. A support arm is associated with the upright and is movable in a direction substantially parallel to the axis of rotation of the wheel. A tool for operating on the wheel is mounted pivoting on the support arm. A sensor, associated with the tool, is able to detect at least one parameter representing contact between the tool and the wheel, said sensor being operationally connected to a control unit able to control an actuator, associated with the support arm, so as to pivot the tool between a first withdrawn position with respect to the axis of rotation of the wheel and a second advanced position with respect to the axis of rotation of the wheel, depending on the at least one parameter representing the contact between the tool and the wheel.