The machine (100) has a cutting head (24) mounted at a lower end of a vertical frame (22). The head comprises a support plate (40) carrying rotary cutting assemblies (26, 28) having parallel rotational axes, where each assembly is provided with two drums. A suction device (34) is connected to a suction nozzle (30) for evacuating spoil earth excavated by the drums. A deflector (200) is arranged above the suction nozzle and attached to the support plate to form a skirt extending laterally on the periphery of the plate to cover one of the drums
