An apparatus for the cutting out of vegetable heads, in particular cauliflower, fruits or parts thereof which have on their underside a central part (stipe), which is to be cut out from the surrounding part along a hemispherical or ogival face. The diameter of the cauliflower is established and the value determined is used for setting and controlling the cutter which is guided on a circular path, for adapting the diameter of the cutter circular path and the penetration depth of the cutter. In addition, the height of the cauliflower to be worked is also sensed, and the values for diameter and height are converted into electric signals and then processed to form setting signals. These setting signals are used for electromechanical control of the cutting operation in such a manner that the adjustment of the diameter of the cutter circular path is carried out independently of the adjustment of the cutter penetration depth.