Apparatus for producing tubular products starting from a tubular body, wherein the apparatus comprises a cutting unit (10) disposed along a directrix of feed (A) of the tubular body to be cut, in order to obtain the tubular products. The cutting unit (10) comprises a rotating arm (11) mounted rotating around a first axis of rotation (Rl), and at least one cutting member (12) mounted rotatable on the arm (11) in such a way as to rotate around a second axis of rotation (R2). The cutting member (12) is able to be moved toward a cutting position, in which the cutting member (12) interacts with the tubular body in order to cut it.