He was the companion and friend of Alexander the Great in his Asiatic campaigns. According to Diogenes Laertius (Lives 9.10.2), in response to Alexander's claim to have been the son of Zeus-Ammon, Anaxarchus pointed to his bleeding wound and remarked, "See the blood of a mortal, not ichor, such as flows from the veins of the immortal gods."
Plutarch tells a story that at Bactra, in 327 BC in a debate with Callisthenes, he advised all to worship Alexander as a god even during his lifetime, is with greater probability attributed to the Sicilian Cleon.
Diogenes Laertius (Lives 9.10.3) also says that Nicocreon, the tyrant of Cyprus, commanded him to be pounded to death in a mortar, and that he endured this torture with fortitude and Cicero relates the same story.
His philosophical doctrines are not known, though some have inferred from the epithet eudaimonikos ("fortunate"), usually applied to him, that he held the end of life to be eudaimonia.