Some authors thinks that the extinction of the Pleistocene megafauna (large mammals such as mammoths, etc.) was contemporaneous with the Younger Dryas (Firestone et al. 2007; Faith & Surovell 2009), while some thinks that it predates it by a couple thousand years (Gill et al. 2009).
Whether or not it was contemporaneous with the Younger Dryas, it constitutes a rather modest extinction event compared to the Big Five (i. e. the five bigger mass extinctions of the Phanerozoic: End Ordovician, Late Devonian, Permian/Triassic boundary, Triassic/Jurassic boundary and Cretaceous/Paleogene boundary, see this previous answer of mine for more details on that), with nonetheless a noteworthy impact (e. g. Johnson 2009) on the remaining ecosystem. The current/future mass extinction is however often considered to be at a comparable scale with these previous five (see for instance Barnovsky et al. 2011), but climate change is not the only one to blame: active destruction of ecosystems, mainly through anthropization, is one major factor as well.
Barnovsky et al., 2011. Has the Earth’s sixth mass extinction
already arrived? Nature, 471: 51-57.
Faith & Surovell, 2009. Synchronous extinction of North America’s
Pleistocene mammals. PNAS, 106(49): 20641-20645.
Firestone et al., 2007. Evidence for an extraterrestrial impact 12,900 years ago that contributed to the megafaunal extinctions and the Younger Dryas cooling. PNAS, 104(41): 16016-16021.
Gill et al., 2009. Pleistocene Megafaunal Collapse, Novel Plant Communities, and Enhanced Fire Regimes in North America. Science, 326: 1100-1104.
Johnson, 2009. Ecological consequences of Late Quaternary extinctions of megafauna Proc. Roy. Soc. B, 276 (1667): 2509-2519.