So We said, "Strike him [i.e., the slain man] with part of it." Thus does Allāh bring the dead to life, and He shows you His signs that you might reason.
(And disagreed among yourselves as to the crime) means, "Disputed."
This is also the Tafsir of Mujahid. `Ata' Al-Khurasani and Ad-Dahhak said, "Disputed about this matter." Also, Ibn Jurayj said that,
وَإِذْ قَتَلْتُمْ نَفْسًا فَادَرَأْتُمْ فِيهَا
(And (remember) when you killed a man and disagreed among yourselves as to the crime) means, some of them said, "You killed him," while the others said, "No you killed him." This is also the Tafsir of `Abdur-Rahman bin Zayd bin Aslam. Mujahid said that,
وَاللَّهُ مُخْرِجٌ مَّا كُنتُمْ تَكْتُمُونَ
(But Allah brought forth that which you were Taktumun) means, "what you were hiding."
The murderer had his supporters who wanted to hide his crime, and hence began accusing different people. But Allah willed that the criminal should be brought to book, and appointed a miraculous way of identifying him -- that is, the dead body of the murdered man should be touched with a part of the flesh of the sacrificial cow. When this was done, the dead man came back to life, announced the name of his murderer, and died again.
This miraculous event is a manifestation of the omnipotence of Allah, and Holy Qur'an presents it as an argument against those who deny the Resurrection of the dead for the Last Judgment. Verse 73 says that this precedent should induce people to make use of their reason, and see that what has happened in a past instance can as easily happen in a future instance.
A murder was committed among the Israelites in Moses’ time. The method that God revealed to His prophet to identify the killer was that an animal should be sacrificed, and the dead man’s corpse be struck with a piece of it. The dead man would then name the murderer. The third lesson in this instance was that life after death is no less a reality than life before death. Just as the dead corpse was revived, so every soul will be raised up in the Hereafter and given new life.
Uthmani text of the Madinah mushaf (King Fahd Complex). Translation: Saheeh International. Tafsir via Quran.com.