Book XV opens on an impossible tree: an undying aśvattha with its roots above and its branches below, its leaves the metres of chant (15.1). Nothing grows that way. The impossibility is the instruction.
What has been turned over is causation. We take the world to be rooted in itself — matter at the bottom, holding everything up, mind a late arrival in it. The image says the root is elsewhere, and above, and that everything we handle as solid is foliage: branches spreading up and down, fed by the strands, with sense-objects for their budding twigs, and further roots reaching down into human action (15.2).
Then the line that startles: this tree, with its roots grown firm, is to be cut — with the strong axe of non-attachment (15.3). Not the world; nobody is being asked to destroy anything. What is cut is the conviction that the tree is self-rooted, which is the same conviction that makes every leaf feel like a permanent address. And the chapter names at once what survives the cutting: a portion of My very self, become the eternal living soul (15.7), seated in the heart of all, from whom come memory and knowing and their loss (15.15).
So the book that begins with an inverted tree ends by counting three: the perishable, the imperishable, and a supreme Person beyond both (15.16–18). The cut is not a loss of a world. It is the discovery of what the world was hanging from.
The tree looks upside down only from where we happen to be standing — out on a branch, among the leaves, certain that down is down. The claim of Book XV is that this is the correct way up, and that a single honest look along the trunk is worth more than any argument about it.