Yes, but you forgot to take account of the cat.
I’m glad everyone has had some fun, but we’ll need now to ask Mods to Close the thread.
Efforts to destroy all life on Earth are probably illegal in many jurisdictions.
Unfortunately they were so busy having fun they failed mention this issue has been formally studied in “The Resilience of Lift to Astrophysical Events”, (Sloan, 2017): The Resilience of Life to Astrophysical Events | Scientific Reports
Besides chance events like a super nova, it would require an asteroid impact massing at least 1.7 x 10^17 kg. There are 19 known asteroids of sufficient mass.
In line with the OP question, could humans deflect such an asteroid and destroy earth. Deflecting asteroids with precision stand-off nuclear detonations has been studied for purpose of saving the earth, and was found possible: “Deflecting Asteroids by Means of Standoff Nuclear Explosions”: http://research.dynamicpatterns.com/wp-content/uploads/2011/03/Deflecting-Asteroids-by-Means-of-Standoff-Nuclear-Explosions.pdf
“Nuclear Explosion Near Surface of Asteroids and Comets - General Description of the Phenomenon”: http://csc.ac.ru/news/1997_1/ae27.pdf
The OP’s scenario would be the opposite – deflecting one of the 19 large asteroids to destroy all life on earth. Since the required asteroid size has been formally studied, there is no theoretical limit to the yield of a nuclear weapon, there’s no limit to the number of detonations possible if humans became obsessed with destroying all life on earth, and since the technology of trajectory calculation and precision fuzing is well understood, it would seem the answer to the OP’s question is yes.