This work aims to investigate the conditions of the occurrence of the phenomenon of ejection of dust grains from mixtures of porous dust-ice agglomerates that may constitute the building material of cometary nuclei. This phenomenon is important for understanding cometary activity, in particular, the formation of the coma. The commonly considered mechanism is the breaking of the dust mantle due to the rise of gas pressure underneath. We consider an alternative process, the detachment of dust grains present on the side surfaces of ice-dust agglomerates due to the flow of water vapor between agglomerates. We take into account the force exerted on dust by vapor, the force of gravity, and the force of friction between the grain and the agglomerate. The latter can be granules, pebbles, cobbles, and boulders. The presented calculations are based on the laboratory measurements of pressure and temperature within samples composed of porous agglomerates of radii from centimeters to decimeters, i.e., pebbles and cobbles. We show that the flow of vapor between ice-dust agglomerates, possibly composing comets, may cause detachment and blowing out dust grains as small as tens of microns in radius, depending on the local size distribution of fragments of material building a comet. The obtained results provide important constraints for models of comet surface evolution and improve our understanding of the role of material structure in controlling the intensity of dust emission.