Little is known about Su's life or career other than his mission beyond the borders of the Western Han involving the
Xiongnu, a mission which turned out to be drastically more trying and lengthy than expected. In 100 BC, there was a short-lived
détente between long-term adversaries the Western Han and the Xiongnu. One year earlier, in 101 BC, a new
chanyu had come to power in Xiongnu, Chanyu
Qiedihou (), who had expressed an interest in peace with the Han and who, as a goodwill gesture, had allowed some Han diplomats who had been detained by the Xiongnu to return to the Western Han, along with gifts from the chanyu. In response, in 100 BC,
Emperor Wu of Han commissioned Su, then the deputy commander of the imperial guards, to serve as an ambassador to Xiongnu. His deputy was fellow deputy commander, Zhang Sheng (), and the third in command was Chang Hui (). However, once they arrived at the Xiongnu chanyu's headquarters, Chanyu Qiedihou was far more arrogant than expected, which angered Zhang. In response, Zhang plotted with two Xiongnu officials, the Prince of Gou () and Yu Chang (), to assassinate Chanyu Qiedihou's half-Han advisor Wei Lü () and kidnap the chanyu's mother. The Prince of Gou and Yu Chang carried out their plot while the chanyu was away on a hunt, but someone alerted the chanyu, who quickly returned and killed the Prince of Gou in battle and captured Yu. Yu admitted to plotting with Zhang. Zhang, alarmed, informed Su, who had been unaware of Zhang's plot. Aware that the chanyu was planning on forcing him to surrender to Xiongnu, Su tried to preserve his dignity by committing suicide with his sword. Wei, who had wanted Su to surrender and become an advisor to the chanyu as well, quickly summoned doctors and was able to just save Su's life. Chanyu
Qiedihou, impressed with Su's heroism, also sent messengers to care for Su's recovery, while putting Zhang and Chang under arrest. After Su recovered, Chanyu Qiedihou decided to publicly execute Yu as an example and to force the entire Han mission to surrender. Zhang became apprehensive and surrendered. Su, however, was not shaken even when Wei put his sword onto Su's neck while Zhang tried to explain that he would be greatly honoured to be the chanyu's advisor. Su rebuked him for his faithlessness to the Western Han and refused to surrender. ==Life in exile==