“What happens if the missile is carrying a nuclear warhead?”
It falls to earth somewhere other than where the enemy wanted it to. It ruins the day for anyone nearby BUT...
It misses its target; that’s the important thing.
Unless the physics package is a gun type assembly (Little Boy), detonation is unlikely, maybe a “fizzle” measured in tons. The laser need not vaporize the target, it could do even as little as damage the re-entry vehicle such that it breaks up when hitting the atmosphere. No explosion, but you do get a few kilograms of fissile dispersed in the atmosphere.