We are causing a major extinction event that is up there with the worst ones the Earth has experienced. That said, the end result is likely to be that we either go extinct or come very close and the remaining life on Earth picks up the pieces and starts re-evolving new biodiversity from the diversity bottleneck.
It's happened before and life on Earth, as whole, will come out the other side of this bottleneck and move on (unless we've tripped some unimaginable feedback loop).
...it's just likely we won't be included in that life.
...and a major extinction event on this scale is nothing to sneeze at either. Really it's chilling enough that we, as a species, are potentially having a similar impact on Earth's biodiversity as the asteroid that killed the dinosaurs. There's really no need to exaggerate that.