A method for collecting the fabric (4) produced by the cylinder (3) of a circular knitting machine, comprising at least the steps of taking down said fabric (4), cutting and collecting it, in which the fabric is cut along a predefined cutting trajectory inclined with respect to the rotation axis ("X") of the cylinder (3). The cutting means (10) are actuated in rotation at a speed differing from the speed of the cylinder (3) of the knitting machine. It is further provided for a circular knitting machine comprising a cylinder (3) turning around a central rotation axis ("X") so as to produce a tubular fabric (4), a take-down and collecting assembly (6) engaging the fabric (4) on the opposite side with respect to the cylinder and equipped with cutting means (10). Said cutting means can be actuated in rotation around the central rotation axis ("X") at an angular speed differing from the speed of the cylinder (3).