Malpighi’s girdling, or tree girdling, is the removal from a stem of a complete external girdle containing the phloem (that is more external) but preserving the xylem (that is more internal).
When a girdle like that is removed below the branches the plant dies because organic food (sugar) is disallowed to pass to the region below the girdle and thus roots die from the lack of nutrients. Since roots die the plant does not get water and mineral salts and dies too.