The world will survive. No matter what humans do. No matter how much we blow up, this floating ball of iron, oxygen, silicon, magnesium, sulfur, nickel, calcium, and aluminium will survive whatever humans could even hope to prevent, and much, much more. In the end our impact will be entirely insignificant on the planet unless we make some massive discoveries in science, which is unlikely.
Life on the other hand.. Humans could destroy it given enough time, but it's most likely we will all die off before that, and even if we tried there are things that would be nearly impossible to destroy. We're much more likely to kill ourselves off first and life would adapt and recover.