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To use the seam ripper, the tailoring bag needs to be empty besides the seam ripper. The seam ripper takes up one inventory slot, and the tailoring bag takes up one bag slot, or can be carried in another bag when empty.
This is no different than the disenchanting cube except you have a built in seam ripper, as the bag can only have one item in it, the item to be destroyed, if you want it to function. It is actually more convenient this way because you only have to carry one thing around instead of the bag+ripper.
Just use a bigger bag in that slot until you need to disenchant.