By reason of him (di' auton). “Because of him,” regular idiom, accusative case with dia.
Went away (hupēgon). Cf. Joh 6:67 for this verb. Inchoative imperfect active of hupagō, “began to withdraw” as happened at the time of the raising of Lazarus (Joh 11:45.) and the secession was still going on.
And believed on Jesus (kai episteuon eis ton Iēsoun). Imperfect active of pisteuō (note aorist in Joh 11:45). There was danger of a mass movement of the people to Jesus.