Machine for extracting puree, or juice, from a food product of vegetable origin, said machine comprising: - a hollow body having a longitudinal axis and an inlet for introducing said food product of vegetable origin, within said hollow body being provided: - a first extraction section providing: - a first sieve positioned into said hollow body and having a first plurality of holes; - a first rotor coaxially positioned within said first sieve and having a first plurality of blades; - a first driving group operatively connected to said first rotor by a first motor shaft and configured to cause said first rotor to rotate within said first sieve to apply a centrifugal force to the product to be treated in order to divide said product to be treated in a first portion, which passes through said first plurality of said first sieve and is discharged through a first outlet and in a second portion, which, instead, does not pass through said first plurality of holes of said first sieve and advances along a direction axial to said hollow body up to reach a passage section; - a second extraction section positioned downstream of said first extraction section and said passage section, said second extraction section being provided with: - a second sieve positioned within said hollow body and having a second plurality of holes; - a second rotor coaxially positioned within said second sieve and having a second plurality of blades, said first plurality of blades of said first rotor and said second plurality of blades of said second rotor being positioned at a predetermined distance (d) from each other; said machine being characterized in that said second extraction section furthermore comprises a second driving group operatively connected to said second driving group by a second motor shaft and configured to cause said second rotor to rotate within said second sieve to apply a centrifugal force to said second portion of said product coming from said first extraction section, in such a way to divide said second portion of said product in a main product, which passes through said second plurality of holes of said second sieve and is discharged through a second outlet and in a waste product, which, instead, does not pass through said second plurality of holes of said second sieve and is discharged through a third outlet; and in that said predetermined distance (d) is less than 500 mm, in such a way that said second portion of said product is arranged to move in said second extraction section without being deteriorated and, at the same time, without damaging the machine. - a hollow body having a longitudinal axis and an inlet for introducing said food product of vegetable origin, within said hollow body being provided: - a first extraction section providing: - a first sieve positioned into said hollow body and having a first plurality of holes; - a first rotor coaxially positioned within said first sieve and having a first plurality of blades; - a first driving group operatively connected to said first rotor by a first motor shaft and configured to cause said first rotor to rotate within said first sieve to apply a centrifugal force to the product to be treated in order to divide said product to be treated in a first portion, which passes through said first plurality of said first sieve and is discharged through a first outlet and in a second portion, which, instead, does not pass through said first plurality of holes of said first sieve and advances along a direction axial to said hollow body up to reach a passage section; - a first sieve positioned into said hollow body and having a first plurality of holes; - a first rotor coaxially positioned within said first sieve and having a first plurality of blades; - a first driving group operatively connected to said first rotor by a first motor shaft and configured to cause said first rotor to rotate within said first sieve to apply a centrifugal force to the product to be treated in order to divide said product to be treated in a first portion, which passes through said first plurality of said first sieve and is discharged through a first outlet and in a second portion, which, instead, does not pass through said first plurality of holes of said first sieve and advances along a direction axial to said hollow body up to reach a passage section; - a second extraction section positioned downstream of said first extraction section and said passage section, said second extraction section being provided with: - a second sieve positioned within said hollow body and having a second plurality of holes; - a second rotor coaxially positioned within said second sieve and having a second plurality of blades, said first plurality of blades of said first rotor and said second plurality of blades of said second rotor being positioned at a predetermined distance (d) from each other; - a second sieve positioned within said hollow body and having a second plurality of holes; - a second rotor coaxially positioned within said second sieve and having a second plurality of blades, said first plurality of blades of said first rotor and said second plurality of blades of said second rotor being positioned at a predetermined distance (d) from each other;