The invention relates to an appliance for cutting food, which includes: a frame (1), a chute (5) for feeding in food, a cutting tool (10) which is mobile in a straight alternating movement, and means (36) for operating the cutting tool (10), which include a transmission system (40). According to the invention, the transmission system (40) includes: an output planet gear (52) which meshes with a stationary output ring gear (51) and which supports a cylindrical conformation (54) for driving the cutting tool (10), as well as a rotatably mobile transmission plate (48) which supports an off-centre rotation shaft (53) of the output planet gear (52), the stationary output ring gear (51) having a diameter that is substantially twice the diameter of the output planet gear (52) and the distance between the rotation shaft of the output planet gear (52) and the axis of the cylindrical conformation (54) being substantially equal to the radius of the output planet gear (52), such that the cylindrical conformation (54) moves along a substantially linear path.