Why does Sophocles have Oedipus blind himself off stage?

Like most truly suspenseful and horrifying moment, whether in theatre, film, or television, what an audience imagines is far more gruesome than anything that they can actually watch. This makes the blinding far more effective offstage.

In addition, as all classical Greek plays were performed with masks, this made it possible for the actor to come back with a different mask to show the change and thus create a visual cue for the audience.

He was blind to all of the warning signs about the path he was travelling because of his Hubris, so he refused to see. He blinds himself so he was literally as blind as he was figuratively.