Atman can not be killed
It cannot be cut.
It cannot be burned.
Atman is eternal.
It goes from one body to another, take different forms.
From Bhagwad Geeta.
atman, is indestructible and eternal (2.18). It neither slays, nor can it be slain (2.19). It is never, born and it never dies. After coming into existence, it never ceases to be. It is nitya (always), sasvatah (permanent) and purana (very ancient) (2.20). It does not suffer, nor can it be tainted. At the time of death it does not die, but leaves the body and enters a new one (2.22). Weapons cannot pierce it, fire cannot burn it, water cannot moisten it and wind cannot dry it (2.23). It is impenetrable, incombustible, all pervading, stable and immobile (2.24). It is invisible, imperceptible and immutable (2.25).
The most important thing is never confuse atman with the soul.
Soul is something which is only in humans, it is debated weather it is women or black people.
Whereas atman is in every living being, its in every animal, its in every living organism. There are more differences between two but this is just basics.
The Brihadaranyaka Upanishad describes Atman as that in which everything exists, which is of the highest value, which permeates everything, which is the essence of all, bliss and beyond description. In hymn 4.4.5, Brihadaranyaka Upanishad describes Atman as Brahman (universal absolute; supreme soul), and associates it with everything one is, everything one can be, one's free will, one's desire, what one does, what one doesn't do, the good in oneself, the bad in oneself.
That Atman (self, soul) is indeed Brahman. It [Ātman] is also identified with the intellect, the Manas (mind), and the vital breath, with the eyes and ears, with earth, water, air, and ākāśa (sky), with fire and with what is other than fire, with desire and the absence of desire, with anger and the absence of anger, with righteousness and unrighteousness, with everything — it is identified, as is well known, with this (what is perceived) and with that (what is inferred). As it [Ātman, self, soul] does and acts, so it becomes: by doing good it becomes good, and by doing evil it becomes evil. It becomes virtuous through good acts, and vicious through evil acts. Others, however, say, "The self is identified with desire alone. What it desires, so it resolves; what it resolves, so is its deed; and what deed it does, so it reaps.
— Brihadaranyaka Upanishad 4.4.5, 9th century BCE