A mechanism (10) includes a slide plate (32) having die openings (38) adapted to hold dies (42a, 42b) and slideable relative to a cooker/extruder (12). Rotary cutters (74) are rotatably mounted relative to and moveable with the dies (42a, 42b). In one preferred form, a motor (76) can be connected and disconnected to the rotary cutter (74) aligned with the cooker/extruder (12) by a male coupling (96) including an elastomeric band (106) tensioned in a groove (102) formed in an outer peripheral surface (100) and received within the inside surface (116) of a cylindrical body (114) of a female coupling (108). Thus, it is not necessary to shut down the cooker/extruder (12) to service or change the dies (42a, 42b) and/or the rotary cutters (74). An annular wear plate (134) is sandwiched between the slide plate (32) and a frame element (18) having a central aperture (126) into which the barrel (14) of the cooker/extruder (12) is slideably received. A center plate (130) extends through the wear plate (134) and is received within the central aperture (126) and is fastened to the barrel (14). Mixer elements (59) are retained in the subpassageways (124) of the barrel (14) by the center plate (130) and can be removed through one of the die openings (38) when the die (42a, 42b) is removed therefrom and without removal of the barrel (14) from the frame element (18).