The long siege of a city is the drawn-out inner effort to master a state of consciousness, and the tree that must be spared is the spine, the trunk of the body up which life and energy rise. However hard the struggle against a fixed mental habit, the central channel that feeds the whole person is never to be cut, because it is the very source that nourishes the one waging the war. The verse names this plainly: the tree of the field is a person's life, the living column in the mind's own terrain.
A person may work relentlessly to overcome an inner condition, yet must never damage the living spinal core through which that same energy flows, since destroying it would starve the very self doing the work.
City: a state of consciousness a person lays siege to and seeks to master.
Tree: the spine, the trunk of the body through which life rises.
Field: the mind, the terrain in which the inner struggle is waged.
Axe: the destructive force that would sever the living channel if turned against it.