Rather than kill him, he allowed the crew to revive Luffy, because (after struggling to remember) they helped apprehend Crocodile (who was doing things beyond his influence as a Warlord) and had a good word put in from captain Smoker. Luffy fought as hard as he could with Kuzan but, ultimately, the battle was ended when Kuzan froze Luffy solid with a single touch. Luffy, grabbed her and gave her to his crew, who then proceeded to revive her using hot water. He then battled the Straw Hats and froze Robin, and was about to smash her when their Captain, Monkey D. Kuzan revealed he knows Luffy's grandfather, which shocked the latter as he compares them before he warned the crew about Robin, who in order to survive due to her excessive bounty and falsified crime listing, betrayed every organization she belonged to. But rather than fighting them immediately, he helped some people who were stranded on an island by freezing the ocean to create a path to another island. One day, the Straw Hat pirates stopped on an island where Kuzan happened to be sleeping. Sometime along the line he was promoted to the position of Admiral. Kuzan expressed remorse for his actions and froze a path out to sea for Robin and giving her a rowboat to escape with. When the Buster Call came to Ohara Island, Jaguar did everything he could to protect Nico Robin, who was the child of a friend of his (who happened to be a wanted criminal for studying the Void Century) but Kuzan froze him solid, killing him.
But Saul was having doubts on the World Government's actions in the name of justice. In his days as a Vice-admiral he had eaten a powerful Logia Devil Fruit that gave him mastery of Ice, he also befriended a giant vice-admiral named Jaguar D. It was also revealed that he looked up to Zephyr very much in his youth, and did things to emulate him like singing Zephyr's favorite song (which he actually hated) and drinking his favorite alcoholic beverage. Not much is known about Kuzan's past, but in the One Piece Film: Z (Non-canon) it was revealed that he, along with other high-ranking Marines, were trained by Admiral "Black-Fist" Zephyr in their early years as marines. Even though Aokiji was an admiral in the navy, which was presented as one of the main antagonistic organizations of the series, he would use his powers and influence to help people rather than be the World Government's force of dominion disguised as justice, and was a strong believer in a Navy concept called, "merciful justice" (which some WG higher-ups called "lazy justice"), and even though he was going to kill one of the main antagonists, the reasons behind it were that he had the means to revive the legendary weapons of ages past which could destroy the world, and he thought that they were too dangerous even for the people who gave him his orders to possess.