I'm not sure about that. Maybe not on the surface, but I could easily see a 40% drop in U.S. agricultural output (number made up) causing massive global turmoil, even potentially leading up to a world war.
Our world is so interconnected that a strong enough shock in one area can arguably start a runaway positive-feedback loop of destruction.
It's certainly possible for an astonishingly large proportion of the population to perish, but extinction requires extermination to be nearly complete.
People in farmland might not be that much better off. Masses of starving, potentially-armed people searching for food will not necessarily be the most respectful of people's property rights. We can expect animal wildlife populations to plummet as they're killed for food, and agricultural output to drop precipitously as supply chains for fuel, fertilizer, and non-terminator-gene seeds go to zero, not to mention as it becomes exceedingly difficult to protect large patches of farmland from raids.
Why? I'd assume that biological warfare could do more, or destroying water/power supplies.
Species can recover even from only a few mating pairs.
It would be catastrophic though.
Ten might as well be zero. 50 people (25 pairs) is necessary with complete control of breeding in order to have sustainable genetic diversity. Without complete control, hundreds are necessary in any given pocket of civilization.
Even if there were tens of millions of humans remaining, there is virtually zero chance of meaningful recovery since all of the low-hanging fruit of industrial-age energy resources have been mined.
You can add the entire nuclear arsenal, super volcanos, meteors, gamma ray burst at will.
Long answer: The effect of volcanic eruptions on climate is somewhat overblown in popular culture. In recorded history, we only have a handful of VEI7 eruptions, and only one within the range of well-recorded history (that one being Tambora). Tambora is known to have been followed by a particularly severe summer, but it was also concurrent with climatic minimums due to the "Little Ice Age" and the solar cycle. Some other VEI7 eruptions are known, but it's highly speculative how severe any sort of climatic was response, both locally and globally.
A supervolcano would be a VEI8 eruption. There are two known VEI8 eruptions in the history of humanity, both well before recorded history. People have claimed that one of these, the Lake Toba eruption, is responsible for a severe bottleneck in human population, but work has shown that a) global ash distribution is identifiable, b) wildlife populations don't seem to have been too affected, and c) even relatively close populations don't seem to have collapsed.
In other words, the largest eruption in the climatic record was incapable of producing an extinction-level event. A Yellowstone caldera eruption wouldn't be all that much larger. For anyone in the ash cloud, it would be problematic for the short term, but that's a relatively short term issue (1-2 years). More serious would be the loss of productive farmland in the US for perhaps a decade or so, but that wouldn't be anywhere near extinction-level for humanity.