How does that work? I'm thinking something to do with the heart. That sounds clean and easy.
Yes, precisely. The heart's cells rely on a difference in net electrical charge between the inside of the cells and the surrounding area outside the cells. By moving electrolytes in and out of the cells, the heart is able to generate and conduct an electrical signal.
If the level of potassium in the blood is too high, there will be no difference in charge between the inside of the heart's cells and the surrounding area outside the cells and the heart will be unable to generate an electrical charge--ie: unable to contract. The heart stops.
The Justice System does it with IV potassium but enough oral potassium supplements ought to do the trick.