At the time of slaughtering, one should recite the tasmiyah in the following manner:
بِسمِ اللهِ وَاللهُ أكْبَر
In the name of Allah Ta’ala, and Allah Ta’ala is the greatest.
عن جابر بن عبد الله رضي الله عنهما قال شهدت مع النبي صلى الله عليه وسلم الأضحى بالمصلى فلما قضى خطبته نزل عن منبره فأتي بكبش فذبحه رسول الله صلى الله عليه وسلم بيده وقال بسم الله والله أكبر هذا عني وعمن لم يضح من أمتي (سنن الترمذي، الرقم: 1521)
Hazrat Jaabir (radhiyallahu anhu) reports, “I was present with Rasulullah (sallallahu alaihi wasallam) at the Eidgah on the occasion of Eidul Adha. When Rasulullah (sallallahu alaihi wasallam) completed the khutbah, he descended from the mimbar (i.e. the raised place upon which he stood to deliver the khutbah) and a sheep was brought before him (for qurbaani). Rasulullah (sallallahu alaihi wasallam) slaughtered the sheep with his own blessed hand while reciting the takbeer بسم الله والله أكبر and saying, ‘This qurbaani is on behalf of myself and those from my Ummah who cannot perform qurbaani (i.e. I convey the reward of this qurbaani to those from my Ummah who cannot perform qurbaani).’”