Generally cylindrical bodies of vegetable matter such as spears of asparagus of varying diameter are telescopically inserted tip end-first into the horizontally radially outwardly opening mouthpieces in a drum that is mounted to rotate on a horizontal axis. A take-in conveyor system running towards the mouthpieces in the loading station, and served by guides which converge toward the individual mouthpieces assist in socketing the bodies in the mouthpieces. Flexible collars in the mouthpieces constrict to grip the end portions of the bodies, and the drum indexes to dispose those bodies so that they project vertically upwards, at the same time bringing a next row of mouthpieces to the loading station. At the cutting station disposed over the drum, pairs of diametrically opposed knives repeatedly descend, engage the bodies and remove strips of peel, the bodies being periodically relatively rotated so that one complete layer of peel is removed from each body before the drum indexes further to a horizontal unloading station. At the latter, the peeled bodies are extracted, arranged, cut cross-wise into sections of uniform length and variable-length remainders and shunted into different collection paths based on microprocessor-stored sensations of relative diameter gained from each of the bodies by sensing how far from a datum the knives in each pair had to close towards one another at the peeling station in order to remove peel from each body.