A capsule processing machine for preparing a beverage from a capsule having a body containing an ingredient, such as a beverage prepared by circulating a liquid into such capsule and centrifugally driving such capsule, comprising: - a holder with a cavity having an upwardly oriented mouth, such as a mouth generally contained in a horizontal plane, for receiving said capsule via the mouth, said capsule having for instance a capsule flange extending generally in parallel to the mouth, optionally the holder being drivable in rotation by a motorized drive axis; and - a cover cooperating with the holder such that the cover and the holder are relatively movable, e.g. manually or automatically, along a movement path from: - an open position for inserting said capsule inbetween the holder and cover into the cavity and/or for removing said capsule from inbetween the holder and cover; to - a closed position for extracting said capsule in the cavity, optionally the cover being associated with a pusher for separating said capsule from the cover in the open position, such as a pusher movable between a retracted position in the closed position and a deployed position in the open position, e.g. a pusher that is resiliently assembled to the cover; and - a capsule transfer device having a capsule guide for guiding said capsule from the holder to a used-capsule evacuation area, e.g. to a used-capsule collector, the capsule guide extending along an evacuation direction and being configured to seize said capsule and hold said capsule above the holder and to guide said capsule towards the evacuation area along the evacuation direction, the movement path and the evacuation direction being at an angle (α 1,α 2,α 3,α 4) favouring a movement of said capsule under the effect of gravity along the capsule guide towards the evacuation area, optionally the capsule guide comprising a wire or stripe or rail, e.g. a grooved rail or a head rail, to form a capsule slide (311,312), characterised in that the capsule guide is tilted during the relative movement of the holder and the cover from the closed position to the open position to reduce said angle (α 1,α 2,α 3,α 4) so as to increase the effect of gravity for moving said capsule towards the evacuation area, the holder and the cover being optionally covered by a lid that is movable from an open position to a closed position by the relatively moving holder and cover or vice versa, e.g. a pivotally mounted lid. - a holder with a cavity having an upwardly oriented mouth, such as a mouth generally contained in a horizontal plane, for receiving said capsule via the mouth, said capsule having for instance a capsule flange extending generally in parallel to the mouth, optionally the holder being drivable in rotation by a motorized drive axis; and - a cover cooperating with the holder such that the cover and the holder are relatively movable, e.g. manually or automatically, along a movement path from: - an open position for inserting said capsule inbetween the holder and cover into the cavity and/or for removing said capsule from inbetween the holder and cover; to - a closed position for extracting said capsule in the cavity, optionally the cover being associated with a pusher for separating said capsule from the cover in the open position, such as a pusher movable between a retracted position in the closed position and a deployed position in the open position, e.g. a pusher that is resiliently assembled to the cover; and - an open position for inserting said capsule inbetween the holder and cover into the cavity and/or for removing said capsule from inbetween the holder and cover; to - a closed position for extracting said capsule in the cavity, - a capsule transfer device having a capsule guide for guiding said capsule from the holder to a used-capsule evacuation area, e.g. to a used-capsule collector, the capsule guide extending along an evacuation direction and being configured to seize said capsule and hold said capsule above the holder and to guide said capsule towards the evacuation area along the evacuation direction, the movement path and the evacuation direction being at an angle (α 1,α 2,α 3,α 4) favouring a movement of said capsule under the effect of gravity along the capsule guide towards the evacuation area, optionally the capsule guide comprising a wire or stripe or rail, e.g. a grooved rail or a head rail, to form a capsule slide (311,312), characterised in that the capsule guide is tilted during the relative movement of the holder and the cover from the closed position to the open position to reduce said angle (α 1,α 2,α 3,α 4) so as to increase the effect of gravity for moving said capsule towards the evacuation area, the holder and the cover being optionally covered by a lid that is movable from an open position to a closed position by the relatively moving holder and cover or vice versa, e.g. a pivotally mounted lid.