A closable opening device having a frame defining a through hole and fitted about a pierceable portion of a sealed package for pourable food products; a removable threaded cap which screws onto the frame to close the hole; and a tubular cutting member screwed inside the hole and rotated by the cap to travel through the pierceable portion. The cutting member has an end cutting edge, in turn having a main blade, and a number of teeth located behind the main blade and decreasing gradually in height so as to act successively on the pierceable portion.