A method and a cleaning device for the mechanical cleaning of a powder, in particular of primary aluminum oxide, direct the powder against a surface in order to strip particulate impurities adhering to the surface of the powder. The aluminum oxide to be cleaned is introduced into a stripping device having a striking mechanism directing the powder with a speed of 20 to 30 m/s several tens of times per second for a time period of <1 to 10 seconds against impact blades rotating in a direction opposite to the striking mechanism The particles of the cleaned, powder-form aluminum oxide having a size of >10 .mu.m are separated from the cleaned, powder-form aluminum oxide having a size <10 .mu.m and the impurities by an air sifter and/or a cyclone and are fed for smelting electrolysis. The powder-form aluminum oxide having a size <10 .mu.m and the impurities are fed to a waste dump or are further processed as raw material.