A method and a machine for rewinding a web (1) for making a log (2a), in particular for the production of rolls of toilet paper, rolls of all purpose wipers or household non woven fabric, industrial rolls and the like. The rewinding is carried out according to the steps of feeding a web (1) of paper into a winding cradle (4); arranging upstream of the cradle (4) a counter support roller (8) comprising at least a cutting slit (9) transversal to the web and a cutting roller (11) with a blade (10) so that it is possible the cut or tear the web (1) for contact of the blade (10) with the web (1); concluding the winding of the log (2a); winding the new log (2b) up to a predetermined length of the web (1); rotating with sliding the counter support roller (8) on the web (1) during the winding of the new log (2b) for causing the blade (10) to cut the web in a desired chosen location.