Wasn't the Sacking of Carthage after the 3rd Punic War?
I'm not sure about the 2nd Punic War, but during the 3rd, and the siege of Carthage, most of the city's population died of starvation and disease from being besieged by the Romans. After the Romans breached the city's defenses, the 6 days of fighting killed many more Carthaginians, while the remaining 50,000 survivors of the city were, as with all sacking of cities during that time period, sold into slavery. The Romans then proceeded to burn the city, and annexed all remaining Carthaginian provinces as the Roman province of Africa.
Scullard, Howard Hayes: A History of the Roman World, 753 to 146 BC.
/u/TEmpTom is correct about what happened- 50,000 Carthaginians (men, women and children) were sold into slavery and Carthage was turned into the Roman province of Africa.
Not all Carthaginians were in Carthage, of course. Some had fled to Numidia in the Third Punic War, for instance, and there were 300 child hostages the Romans had been given earlier that who we may hope lived out their lives relatively peacefully.
Carthaginian culture lived on, though. Punic was still spoken in the region around Hippo Regius about five and a half centuries later, as attested to by St. Augustine. Punic remained in use among the Libyans and Numidians, who used it on the many inscriptions in their temples, tombs, public buildings and other places. Carthage's gods were Latinised: Baal Hammon became Saturn, Tanit became Juno Caelestis. Important people kept their Carthaginian names, even down to Augustus' day!
D. Hoyos, "The Carthaginians" (Routledge, 2010)