Sayyiduna Umar bin al-Khattab (may Allah be pleased with him) says that slaughtering should be done between the throat and the labbah, and do not hasten the souls before they depart.
This has also been narrated as marfu' through a weak route, and it is of no worth.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الضحايا / 19124