Hadith: Indeed, Allah has enjoined Ihsān (kindness/excellence) in all things

عَنْ أَبِي يَعْلَى شَدَّادِ بْنِ أَوْسٍ رَضِيَ اللَّهُ عَنْهُ عَنْ رَسُولِ اللَّهِ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ قَالَ:
«إِنَّ اللهَ كَتَبَ الْإِحْسَانَ عَلَى كُلِّ شَيْءٍ، فَإِذَا قَتَلْتُمْ فَأَحْسِنُوا القِتْلَةَ، وَإِذَا ذَبَحْتُمْ فَأَحْسِنُوا الذِّبْحَةَ، وَلْيُحِدَّ أَحَدُكُمْ شَفْرَتَهُ، وَلْيُرِحْ ذَبِيحَتَهُ».
[صحيح] - [رواه مسلم] - [الأربعون النووية: 17]

Abu Ya‘la Shaddād ibn Aws (may Allah be pleased with him) reported that the Messenger of Allah (ﷺ) said:
"Indeed, Allah has enjoined Ihsān (kindness/excellence) in all things. So, when you kill, kill with kindness; and when you slaughter, slaughter with kindness. Let one of you sharpen his blade and spare the animal he slaughters suffering."
[Authentic hadith] - [Narrated by Muslim] - [الأربعون النووية - 17]

Explanation

The Prophet (may Allah's peace and blessings be upon him) informs that Allah Almighty prescribed ihsān (kindness/excellence) upon us in everything. Ihsān: It is constantly being heedful of Allah in worshipping Him, doing good, and abstaining from harming other created beings. An aspect of this is ihsān in killing and slaughtering.
Ihsān in killing, for legal retribution, is to choose the easiest method which causes the least suffering to the one being killed and the quickest in taking his life.
Ihsān in slaughtering animals is to show kindness toward the animal by sharpening the blade and not sharpening it while the animal is looking on, and not slaughtering an animal while another animal is looking.

Benefits from the Hadith

1. The Hadīth shows Allah's mercy and kindness toward His creation.
2. Ihsān in killing and slaughtering is to do it in the manner prescribed by the Shariah.
3. The Shariah is perfect and comprises all forms of goodness, one of which is mercy and kindness toward animals.
4. It is prohibited to mutilate a person after killing him.
5. Anything that causes suffering to animals is prohibited.