A plant (1) for cold extraction of puree, or juice, from a fresh food product of vegetable, or animal origin, includes a treating machine, for example a softening machine (20) downstream of which an extraction machine (30) is provided for extracting juice, or puree, from the food product of vegetable, or animal origin. Upstream of the treating machine (20) a cutting machine is provided (40,40′) in which a cutting means is arranged to cut the starting food product of vegetable origin into parts of predetermined size. More in detail, the cutting means (40) is arranged to cut the vegetable product (100) into parts (105) of size set between 50 mm and 130 mm, which are then fed to the treating machine (20).