A process that is capable to optimize the efficiency of extraction at room temperature of juice or puree from food pulps of fruit and vegetables, responsive to the consistency of the same. In a first step the pulps are cut and softened in a first section ( 4 ) of the machine, where a first rotor ( 5 ) applies to the food pulps a plurality of pulses in quick succession against a stator that has protrusions on the inner surface. The softened product then passes through a second section ( 6 ), where the separation is carried out of the part of pulp that can be used (juice or puree), which are conveyed in a outlet duct ( 11 ), from the waste solid parts (peelings, seeds, hard fibres), which are disposed through an outlet ( 13 ). The rotors ( 5, 7 ) are not mounted on a same shaft, but on different shafts ( 8, 18 ) operated by respective motors ( 9, 19 ). Both motors ( 9, 19 ) are operatively connected to a device ( 20 ) that controls the respective speeds in a manual way, for example by a speed variator, or automatically, responsive to predetermined input parameters, relative to the consistency of the product.