Yes, Kratos is mortal in the sense that he can be killed by more conventional means(although they have to be pretty powerful).
For a God, or immortal, like Zeus, it takes powerful artifacts like Pandora's Box or the Blade of Olympus, since they possess Godly power within them.
EDIT: Although that raises the question of how the fvck Kratos killed the Sisters of Fate? Are they not true immortals then?
I don't think he killed them, but trapped them in a mirror. Because...Clotho was killed by getting impaled in the head (and in the myths Zeus got his hea split, and he was fine and dandy).
Anyway, immortal is different from being invincible.
Off-topic: That Star-Destroyer thing Starkiller pulled down, is they it as big as a Titan (a Titan is 2x taller than the Empire State Building, and as for the Colossus Statue...it fits into a Titan's hand--talking gameplay scale--and they are 6x the size of a God)?