The machine (10) has a turbine (12) mounted in a casing (14) and provided with large vanes (12C) and small blades (12D). The turbine permits suction of air to intake wastes i.e. dead leaves, via an inlet (14A) of the casing of the turbine and to evacuate the wastes via an outlet (14C) of the casing of the turbine. A drive device i.e. motor, drives the turbine. A stop system disconnects the turbine from the drive device, and stops rotation of the turbine. A damping layer (90) is interposed between an outer wall (14G) and an inner wall (88) of the casing.