hi! while there are a few anthropologists here, it might be worth x-posting this question to our sister sub, /r/AskAnthropology, as this question would be right up their street

This depends on your definition of "mass extinction." The most recent of the "big five" occurred 65 million years ago, and those are generally considered to be the so called "mass" extinctions. I suspect you mean extinction event, which have occurred. The ice age, which has been going on for the majority of human history, has lead to numerous extinction events, usually at the beginning or just after the end of a glacial period, which is what most people think of when they think ice age.

The most recent such event is called the younger dryas, which was a period, around 12,000 years ago where the pattern of warming that existed up until relatively recently (that has now continued because of global warming) during our current interglacial period reversed for about 1300 years. This event is thought to be one of the main causes of the extinction of most North American megafauna, such as the mammoths and giant ground sloths.

Another notable extinction event was the Mount Toba supervolcanic eruption, about 70,000 years ago. There is a genetic bottleneck in the human population which has been traced to this time period. Located in Indonesia, this eruption is the most recent supervolcanic eruption. This has also been proposed to be the cause of the disappearance of a few species, including Gigantopithecus, the largest ever primate.

If you begin to count things caused by humans, the number of events skyrockets. The disappearance of many large animals in Australia including giant wombats called diprotodon, 8 ft tall kangaroos called Procoptodon, and a giant monitor lizard, similar to the komodo dragon, but larger, called megalania. All of these disappeared about 45,000 years ago, shortly after the arrival of human in australia. These are thought to have been killed by humans, directly or through destruction of prey species.