The beater mill (1), to reduce objects and/or materials into fragments, has a container (2) for them with an inner circular inner wall (4). A shaft (5) is through the container, with a head (6) where a beater (7) rotates around it with a number of beating units (18) moving against each other. An insert (8), with a truncated cone shape, is in the container under the beater rotating around the shaft. The insert has a wall (9) against the container inner wall with projecting beaters towards the inner wall.