The splicing device (7) for splicing a trailing edge of a first web material (N1) to a leading edge of a second web material (N2) comprises members (41, 43) defining a feed path of the web material (N1, N2). The device also comprises a first cutting member (59) and a second cutting member (61), cooperating with the first cutting member. One of the two cutting members (59,61) is provided with a movement transverse to the feed path of the web material, to move the cutting member (61) from an operating position, in which it is in front of the other cutting member (59), to an idle position, withdrawn with respect to the feed path of the web material.