Is the Younger Dryas associated with an extinction event?
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 &amp; 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.

References:
Barnovsky et al., 2011. Has the Earth’s sixth mass extinction
already arrived? Nature, 471: 51-57.
Faith &amp; 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.