During slaughter, the Prophet (ﷺ) would say this -
بِسْمِ اللَّهِ وَاللَّهُ أَكْبَرُ هَذَا عَنِّي وَعَمَّنْ لَمْ يُضَحِّ مِنْ أُمَّتِي
Transliteration
Bismillah-hi wallahu akbaru haza 'anni wa amman lam udahh-hi min ummati
Translation
In the name of Allah, Allah is Most Great. This is from me and from those who did not sacrifice from my community.
حَدَّثَنَا قُتَيْبَةُ بْنُ سَعِيدٍ، حَدَّثَنَا يَعْقُوبُ، - يَعْنِي الإِسْكَنْدَرَانِيَّ - عَنْ عَمْرٍو، عَنِ الْمُطَّلِبِ، عَنْ جَابِرِ بْنِ عَبْدِ اللَّهِ، قَالَ شَهِدْتُ مَعَ رَسُولِ اللَّهِ صلى الله عليه وسلم الأَضْحَى بِالْمُصَلَّى فَلَمَّا قَضَى خُطْبَتَهُ نَزَلَ مِنْ مِنْبَرِهِ وَأُتِيَ بِكَبْشٍ فَذَبَحَهُ رَسُولُ اللَّهِ صلى الله عليه وسلم بِيَدِهِ وَقَالَ " بِسْمِ اللَّهِ وَاللَّهُ أَكْبَرُ هَذَا عَنِّي وَعَمَّنْ لَمْ يُضَحِّ مِنْ أُمَّتِي " .
Translation
Narrated Jabir ibn Abdullah: I witnessed sacrificing along with the Messenger of Allah (ﷺ) at the place of prayer. When he finished his sermon, he descended from his pulpit, and a ram was brought to him. The Messenger of Allah (ﷺ) slaughtered it with his hand, and said: In the name of Allah, Allah, is Most Great. This is from me and from those who did not sacrifice from my community. [Sahih (Albani). Abu Dawud: 2810]
This qurbani niyat brings Allah's acceptance and blessings. Your sacrifice during eid ul adha festival becomes more meaningful.
The dua for sacrificing animal is Allahumma taqabbal minni kama taqabbalta min khalilika Ibrahim wa habibika Muhammad. Say this qurbani dua before you sacrifice on Eid ul Adha.
Say Bismillah Allahu Akbar before you slaughter. This is the qurbani dua in Arabic. It is important for your qurbani niyat on Eid day.
Say Bismillah Allahu Akbar, then Allahumma hadha minka wa laka, hadha anni. This is the correct dua for sacrificing animal during Eid ul Adha festival of sacrifice.
Say Bismillah Aqeeqatu fulan, then Allahumma minka wa laka. This is different from qurbani dua but you still say it before aqeeqah sacrifice.
You can say O Allah, I hope for Your mercy. Don't leave me even for a moment. Fix all my affairs. This is not qurbani dua but is good for dhikr and seeking Allah's help.