How does ADH (vasopressin) cause hyponatremia?

ADH (vasopressin) Antidiuretic hormone prevents diuresis which causes fluid retention which causes dilution of electrolytes, including sodium, hence low level.
See below. Too much ADH (vasopressin) (antidiuretic hormone) prevents the release of water from the body. This retained water dilutes the salts in the body. As sodium is the most abundant, hyponatremia results.