Don't be silly. Of curse He is a Savior. Christ, by His death, offered heavenly citizenship to all mankind. You don't expect Him to fill out your application and carry your luggage as well, do you?
For what its worth, here’s a link to Kontakion 22 of +Romanos the Melodist (8th century) which, as its name indicates, outlines the Victory of the Cross. It is a poetic explication of Orthodox theology on the purpose of the crucifixion. Its a pdf file. Its really worth the read.
http://www.anastasis.org.uk/ROMK22.pdf