Without even seeing who his opponent is Thor immediately goes into the fetal position and whimpers in anticipation of the beating to come. Superman, upon seeing this pathetic scene, places his hand softly, but firmly over Thor's mouth. Thor weakly claws a bit at Supermans hand, but gives in, knowing it's for the best.
Thus did Superman break his no kill rule and suffocate Thor to death. When asked how he justified killing a poor helpless nothing like that, he said that it was a mercy killing, much like putting a dog or horse out of it's misery. To let Thor live would have been infinetly more cruel than to end his suffering.