A machine (1) for extracting puree, or fruit juice, from a product of animal or vegetable origin, provides a hollow body (10) having a longitudinal axis (101). In the hollow body (10) a sieve (30) is mounted having a plurality of holes (35), in order to result co-axial to the hollow body (10) same. The machine (1) also comprises a rotor (40) mounted coaxially in the sieve (30) and having a plurality of blades (46) arranged to cause a centrifugal force to the product to treat, in order to separate it into a main product that crosses the sieve (30) and that is discharged through a first outlet (5) and into a waste material that, instead, cannot cross the sieve (30) and is discharged through a second outlet (6). Furthermore, a distributor (70) is provided integral to the hollow body (10) and arranged to receive the product for distributing it to the rotor (40). A support frame (300) of the sieve (30), or "sieve cage", is also provided to which the sieve (30) is integral. The support frame (300) comprises a plurality of coaxial ring portions (305) connected by a predetermined number of connecting portions (320', 320", 320"').