How did St. Dymphna die?

I believe she was killed by her mentally ill father.

The following excerpt is from the Catholic Encyclopedia. Please note that it is a legend, and identical with many pagan legends also found at the time. So we probably do not know the real story, only that she did exist and that many miracles have been attributed to her.

According to the narrative, Dymphna - the daughter of a pagan king of Ireland - became a Christian and was secretly baptized. After the death of her mother, who was of extraordinary beauty, her father desired to marry his own daughter, who was just as beautiful, but she fled with the priest Gerebernus and landed at Antwerp. Thence they went to the village of Gheel, where there was a chapel of St. Martin, beside which they took up their abode. The messengers of her father however, discovered their whereabouts; the father betook himself thither and renewed his offer. Seeing that all was in vain, he commanded his servants to slay the priest, while he himself struck off the head of his daughter. The corpses were put in sarcophagi and entombed in a cave where they were found later. The body of St. Dymphna was buried in the church of Gheel, and the bones of St. Gerebernus were transferred to Xanten