Tearing:

It is permitted to tear any item for the need of the Holiday. It is forbidden to tear without need for the Holiday, unless all the following conditions are met:

One’s intent is to destroy the item.

The item is not attached to the ground,

The item is a single entity as opposed to being combined from different materials.

The tearing does not involve the work of a professional.

May one cut toilet paper? This may be done for use during the Holiday.

May one sell fabrics or other materials which are required to be cut? They may only be cut if it they have a need for the Holiday. However, there are Poskim who rule this is permitted to be done.

May one cut a piece of paper for no reason? Yes, it may be cut as long as one does not intend to cut it to any specific measurement.

Separating items which have been taped or glued together: Have the same law as tearing, as explained above.