A self-propelled construction road milling machine, includes a machine frame and a milling drum housing, in which a milling drum is arranged. The machine includes a drive unit with which the height of the scraper blade of a scraper device can be adjusted in relation to the milling drum. A control unit for the drive unit adjusts the height of the scraper blade and a measurement device measures the distance between the lower edge of the scraper blade and the milled material. The control unit is designed in such a way that the scraper blade is height-adjustable depending on the height of the milled material remaining in the milled track. The control unit ensures that, on the one hand, the milled material can come out of the milling drum housing unimpeded behind the milling drum in the direction of work and, on the other hand, that the milling drum housing is shut above the material that is coming out. On the one hand, an unimpeded operation of the milling machine is thus ensured and, on the other hand, a clean result of the work is achieved.