We study the quasiclassical magnetotransport of noninteracting fermions in two dimensions moving in a random array of strong scatterers (antidots, impurities, or defects) on the background of a smooth random potential. We demonstrate that the combination of the two types of disorder induces a novel mechanism leading to a strong negative magnetoresistance, followed by the saturation of the magnetoresistivity ρxx(B) at a value determined solely by the smooth disorder. Experimental relevance to the transport in semiconductor heterostructures is discussed.