It can be done after the tuber shows signs of life and is starting to sprout, but it's not always successful, there's a good chance of rot or disease setting in. I would only try cutting the tuber in half and only if you can see developing eyes on both halves. It's much safer to take cuttings. If you do decide to take a chance, dust the cut with something like flowers of sulphur and let the cut heal completely before planting.

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