When Genghis wanted to slaughter people, he could do it really well, but he wasn't that crazy. When he took power and became the one true leader of the mongols at the end of the twelfth century, the first thing he done was take revenge on the northern Chinese states of Xi Xia and Jin (which was itself taken over by mongols a century earlier). They showed no mercy to the Chinese for the Chinese were their arch enemies and thus you could expect a brutal slaughter.
However, prior to laying the Khwarezmid Empire to waste, all Genghis wanted to do was form a trade relationship with them. Thrice Genghis tried to form a trade agreement, on the last occasion even sending between 100-450 people who were all massacred by the Khwarezmid leader, Shah Ala ad-Din Muhammad. Only after this did Genghis seek revenge, resulting in the slaughter of over a million people.
Genghis was relatively cool and calculated. At that point in time, he didn't want to rule over the Khwarezmid because he was concerned that the extension of the mongol border would further divide his troops and resources, leading to the weakening of the mongol empire. He was certainly brutal, but he wasn't really a "crazy savage ass mother fucker".