Your sentence is confusing because you use the neutral pronoun "it", which in English is used to describe things. Unless you're talking about some kind of living being (like an animal or plant), things don't have a life to end. We can talk metaphorically about ending the life of something like a rock, but without the proper context it can sound bizarre.
Assuming the proper context where you explain the "life" of this inanimate it, then "in the manner of (a) permanent death" makes a kind of sense with or without the "a". Still, "permanent death" is a meaningless phrase. When is death not permanent? And how is action that works in the manner of ending something's existence any different from simply ending its existence?
My point is that I suspect you're trying to force a direct translation from your native language into English, but the words you choose do not carry the same meaning or nuance. As FumbleFingers says in his comment, acting "in the manner of" something means to imitate that thing -- but if you end something's existence then there is no imitation about it. It's either dead or not dead. There is no in-between (except perhaps in metaphysics, but that's a different topic).
I hope you can appreciate our confusion. Nevertheless, as an attempt to answer your question:
When talking about "completely ending something's existence" it would be better (or at least more elegant) to use available vocabulary that leaves no doubt in the reader's mind what you mean:
and possibly (depending on context):
- wipe out
and others. English has a great many words that refer to getting rid of things.
Much depends on what "it" is in your example sentence. You can annihilate a particle of matter, you can eliminate a pestilent bacterium, you can liquidate an asset, you can obliterate any reference to a historical event, and so on.
Suppose you are writing a philosophical/religious tract, and in this case "it" is the egotistical attachment to the material world, which various beliefs say is the root of existential suffering. You might then want to say that you woke up one day with the desire to eradicate this attachment -- which is to say, to completely remove it from its place in your psyche. Other possible verbs: expunge, purge, expurgate, extirpate, expel, purify, eliminate, and various others.
Or suppose you are talking about the paranormal, and the thing you want to end the existence of is a ghost that has been haunting your house. In this case English has the wonderfully specific verb exorcise, which means "to drive out an evil spirit".
Anyway, these are just some random examples that (more or less) fit your context. If you want to provide more specifics, I could probably write a more useful answer.