Verse 6.11.1-2

अस्य सोम्य महतो वृक्षस्य यो मूलेऽभ्याहन्याज्जीवन्स्रवेद्यो मध्येऽभ्याहन्याज्जीवन्स्रवेद्योऽग्रेऽभ्याहन्याज्जीवन्स्रवेत्स एष जीवेनात्मनानुप्रभूतः पेपीयमानो मोदमानस्तिष्ठति ॥ ६.११.१ ॥
अस्य यदेकां शाखां जीवो जहात्यथ सा शुष्यति द्वितीयां जहात्यथ सा शुष्यति तृतीयां जहात्यथ सा शुष्यति सर्वं जहाति सर्वः शुष्यति ॥ ६.११.२ ॥

asya somya mahato vṛkṣasya yo mūle'bhyāhanyājjīvansravedyo madhye'bhyāhanyājjīvansravedyo'gre'bhyāhanyājjīvansravetsa eṣa jīvenātmanānuprabhūtaḥ pepīyamāno modamānastiṣṭhati || 6.11.1 ||
asya yadekāṃ śākhāṃ jīvo jahātyatha sā śuṣyati dvitīyāṃ jahātyatha sā śuṣyati tṛtīyāṃ jahātyatha sā śuṣyati sarvaṃ jahāti sarvaḥ śuṣyati || 6.11.2 ||

1-2. O Somya, if someone strikes at the root of a big tree, it will continue to live, though it may exude some juice. If he strikes at the middle, it will still live, though it may exude some juice. If he strikes at the top of the tree, it will survive, though it may exude some juice. Pervaded by the self, the tree will keep drinking juice and living happily. But if the self leaves a branch of a tree, that branch withers away and dies. If it leaves a second branch, that branch too will die. If it leaves a third branch, that branch also will die. If the self withdraws from the whole tree, then the whole tree will die.

Word-for-word explanation:

Somya, O Somya; asya mahataḥ vṛkṣasya, of this big tree; yaḥ mūle abhyāhanyāt, [if] a person strikes at the root; jīvan, it [the tree] continues to live; sravet, [though] it exudes juice; yaḥ madhye abhyāhanyāt, [if] a person strikes in the middle; jīvan, it [the tree] continues to live; sravet, [though] it exudes juice; yaḥ agre abhyāhanyāt, [if] a person strikes at the top; jīvan, it [the tree] continues to live; sravet, [though] it exudes juice; saḥ eṣaḥ, this [tree]; jīvena ātmanā anuprabhūtaḥ, is pervaded by the living Self; pepīyamānaḥ, it continues drinking; modamānaḥ tiṣṭhati, [and] living happily, Yat, if; jīvaḥ, the self [life]; asya ekām śākhām, one branch of it [the tree]; jahāti, abandons; atha, then; sā śuṣyati, it [the branch] withers away; dvitīyām, a second [branch]; jahāti, [if] it leaves; atha sā śuṣyati, then it [the branch] withers away; tṛtīyām, a third [branch]; jahāti, [if] it leaves; atha sā śuṣyati, then it [the branch] withers away; sarvam jahāti, [if] it leaves all [the whole tree]; sarvaḥ śuṣyati, the whole tree withers away.

Commentary:

Suppose you strike at a tree. If the tree is not dead, water will come out of the wound, and eventually the wound will heal. According to Vedānta, a tree is a living individual, like a human being. It has life; it has a self. As my self permeates the whole of my body, similarly, the self of a tree permeates the whole body of the tree.

If one part of my body becomes paralyzed, it means that the self which previously permeated the whole of my body has withdrawn itself from that part. So also, if the self of a tree leaves a limb of the tree, that limb becomes dried up.

The Upaniṣad is trying to say here that death merely means the withdrawal of the individual self from the whole body. Suppose you are living at a certain house. If you leave that house and move somewhere else, that house becomes vacant and useless. It’s exactly like that. When the Self leaves the body, the body becomes empty and useless.