Aslaam mualykom warahmatula wabarakaatu,
You have not given a specific question or motivation for it I can only assume you are referring to the following:
“Whoever kills a [innocent] person it is as though he has killed all mankind. And whoever saves a life, it is as though he had saved all mankind.” (Quran 5:32)
This is in reference to killing innocent Humans. However there are hadith listed below refering to killing of animals for no resason.
The manner in which we slaughter animals is a merciful manner if you compare it to the way in which the kufaar (non-believers )slaughter animals is very vicious and not very merciful at all. We slaughter in accordance with the Sunnah of Rasululah Muhammad and the direction of the Holy Quran.
Prohibited to you are dead animals, blood, the flesh of swine, and that which has been dedicated to other than Allah , and [those animals] killed by strangling or by a violent blow or by a head-long fall or by the goring of horns, and those from which a wild animal has eaten, except what you [are able to] slaughter [before its death], and those which are sacrificed on stone altars, and [prohibited is] that you seek decision through divining arrows. That is grave disobedience. This day those who disbelieve have despaired of [defeating] your religion; so fear them not, but fear Me. This day I have perfected for you your religion and completed My favor upon you and have approved for you Islam as religion. But whoever is forced by severe hunger with no inclination to sin - then indeed, Allah is Forgiving and Merciful.(Quran 5:3)
O you who believe! Eat of the good things that We have provided for you and be grateful to Allah, if it is Him that you worship (Quran 2:172)
So eat of that [meat] upon which the name of Allah has been mentioned, if you are believers in His verses.And why should you not eat of that upon which the name of Allah has been mentioned while He has explained in detail to you what He has forbidden you, excepting that to which you are compelled. And indeed do many lead [others] astray through their [own] inclinations without knowledge. Indeed, your Lord - He is most knowing of the transgressors.(Quraan 6:118 - 119)
“And We have sent you O Muhammad not but as a mercy for all of humankind, jinn, and all that exists.” (Quran 21:107)
There a many hadith that refer to the slaughter of animals:
Shahi Bukhari: Volumn 007, Book 068, Hadith Number 454.
Narated By Anas bin Malik :
The Prophet said, "Whoever slaughtered the sacrifice before the prayer, he just
slaughtered it for himself, and whoever slaughtered it after the prayer, he slaughtered it at the right time and
followed the tradition of the Muslims."
Volumn 007, Book 068, Hadith Number 461.
Narated By Anas : Allah's Apostle came towards two horned rams having black and white colours and slaughtered
them with his own hands.
Other hadith books:
"Allah has ordained kindness (or excellence) in everything. If killing is to be done, do it in the best manner, and when you slaughter, do it in the best manner by first sharpening the knife, and putting the animal at ease" (hadith narrated by Muslim).
"If someone kills a sparrow for sport, the sparrow will cry out on the Day of Judgement, 'O Lord! That person killed me in vain! He did not kill me for any useful purpose" (Nisai).
"Whoever kills a sparrow or anything bigger than that without a just cause, Allah will hold him accountable on the Day of Judgement. The listeners asked, O Messenger of Allah, what is a just cause? He replied, That he will kill it to eat, not simply to chop off its head and then throw it away" (Nisai, Hakim).
I hope this answers your question.