I would not try breaking the handle off. Better to try to get the superglue into the crack. Get the thinnest super glue you can and it should go right into the crack via capillary action. That may be enhanced by picking the cup up by the handle so the crack widens ever so slightly. Might do it with water in the cup. Once the glue wicks into the crack then use a strong rubber band to exert pressure on the joint and leave it that way overnight. Ultimately, the handle will likely fail especially after many dishwasher cycles. Would be safer to retire the cup to a display shelf.
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