The possibility of destruction carbonaceous dust particles swept out by the radiation pressure into near-galactic space due to the relative motion of dust particles of various sizes is considered. The earlier model of the motion of dust in the Galaxy under the action of radiation pressure, gravity, and gas resistance is expanded taking into account the destruction processes. The possibility of dust sweeping is considered taking into account its collisions with the gas of the Galaxy and with other dust particles. Also, we clarify the range of particle sizes that can get into intergalactic space due to the described mechanism.