MOSCOW—Those who do not know the character of former President of Georgia Mikheil Saakashvili may have been shocked at the scene in Kiev, Ukraine, on Tuesday. Passionate and charismatic by nature, Saakashvili always felt in his element leading crowds of supporters to quick and colorful victories. On Tuesday, Saakashvili, 49, climbed up the rooftop of his apartment building just off Maidan Nezalezhnosti, the famous square that was the epicenter of Ukraine’s revolution in the winter of 2013-2014. “Poroshenko is a thief!” shouted Saakashvili from the rooftop, denouncing his former ally, the billionaire president of Ukraine, Petro Poroshenko. “He is a...