Girdling results in the removal of the phloem, and death occurs from the inability of the leaves to transport sugars (primarily sucrose) to the roots. In this process, the xylem is left untouched, and the tree can usually still temporarily transport water and minerals from the roots to the leaves.
Why would tree girdling eventually cause a tree to die?
The reason for damage due to girdling is that the phloem layer of tissue just below the bark is responsible for carrying food produced in the leaves by photosynthesis to the roots. Without this food, the roots ultimately die and cease sending water and minerals to the leaves. Then the leaves die.
How long does it take for a girdled tree to die?
Be patient when looking for the results, as the tree will appear fine until the need for nutrients from the roots becomes great in the following spring. Sometimes it might take two years for the tree to die.