Device for discarding trims formed by cutting machines during the cutting of paper logs, comprising an advancing plane on which paper rolls (R) and trims (RT, RC) advance along a given direction (A), wherein the trims can fall through a discontinuity provided on said advancing plane. The said advancing plane is formed by a first extendible conveyor (1) and a second extendible conveyor (2). Each of said conveyors (1, 2) is connected with extension and retraction means. The said discontinuity on the advancing plane is realized or eliminated depending on the extended or not extended configuration of said conveyors (1, 2).