All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The Prophet sacrificed and ordered the Muslims to sacrifice. Al-Bukhari and Muslim reported from Anas that he said: “The Prophet slaughtered – as sacrifice – two rams, black and white in color, and I saw him putting his foot on their sides and mentioning Allah's Name and Takbeer (Allahu Akbar). Then he slaughtered them with his own hands.”
Al-Bukhari and Muslim also reported from Jundub Al-Bajali that he said: “I witnessed the Prophet praying on ‘Eed Al-Adh-ha, then he delivered the Khutba saying: “Whoever slaughtered the sacrifice before he prayed should offer a sacrifice in lieu of it and whoever has not slaughtered it, should slaughter mentioning Allah's Name.” But this order is supererogatory not compulsory.
So, we Muslims slaughter sacrifices following our Prophet and abiding by his orders.
Moreover, our beloved Prophet ordered us to follow the example of Prophet Ibraheem (Abraham) in particular as Allah Says (what means): {Then We revealed to you, [O Muhammad], to follow the religion of Abraham, inclining toward truth; and he was not of those who associate with Allah.} [Quran 16:123]
Allah also Ordered us to abide by the orders of other Prophets in general. Allah Says (what means): {Those are the ones whom Allah has guided, so from their guidance take an example.} [Quran 6:90]
Allah knows best.