Based on a Naaleh.com shiur by Rabbi Shimon Isaacson
In order to violate the Torah prohibition of Koreah, tearing, one must do so for the sake of Tofer, sewing. This law is derived from the times of the Mishkan. Moths would eat circular holes into the curtains. These holes were hard to mend. They needed to be torn into a kind of line to be sewn up. This is an example of destructive action that is transformed into constructive action. Most poskim agree that tearing for a constructive purpose, although not for the sake of Tofer, is still a Torah prohibition of Koreah.
·Tearing open the sewn-up pocket of a new garment is prohibited on Shabbat.
·According to the Mishna Berura, one may not slit a sealed envelope open on Shabbat.
·Ripping paper towels, garbage bags, or toilet paper from a roll involves not only Tofer, but also Mechatech, cutting to a specific size. The accepted custom is to use pre-cut bags and tissues on Shabbat. In a situation involving human dignity, rabbinic prohibitions are waived. Therefore, tearing toilet paper with a shinui (in an unusual manner), is permissible when there are no other options, as long as it is not torn on the perforated lines.
·Opening food packages in a destructive way (being careful not to tear any printed letters) is permitted on Shabbat.
·Opening the tab on a closed cereal box is both Mechatech and Koreah. The box should be opened at the side or from another area which does not involve ungluing or tearing the perforation. The best solution would be to open it before Shabbat.
·One may not separate the pages of a new book on Shabbat. This involves Koreah in addition to Makeh B’patish.