A dispenser device for fluid or powder, including an air expeller (20) and a reservoir (30). The reservoir (30) has an air inlet (31) connected to the air expeller (20) and a composition outlet (32) connected to a dispenser opening (10), and is removably mounted on the air expeller. After actuation, the empty reservoir can be removed from the air expeller and replaced with a new reservoir. The air inlet (31) is closed by a first closure element (40) and the composition outlet (32) is closed by a second closure element (50). A mechanical opening system (61, 62) co-operates with the first and second closure elements to expel each closure element from the closed position. The mechanical opening system has a first rod (61) secured to the air expeller (20), and a second rod (62) secured to the dispenser head (1), co-operating with a closure element during actuation.