We can’t destroy the planet per se, but we can do a pretty good job of wiping life off it with a full scale nuclear war.
But the planet will still be there, floating around the sun like usual. Just no humans left on it. There’ll be just cockroaches, bacteria and stuff like that, but the globe – the actual planet, will not break up or crack or anything like that.
And Earth will rebound eventually, maybe better off without us. We’ve had five extinction events already on Earth, what’s another one? It just means life has to start over. Happened before. Nuclear war or asteroid, it will probably happen again.