What is the difference between doing so and so doing?

Answer 1

The difference is one of usage, since they actually mean the same: 'doing that'. (There is a similar difference between 'saying so' and 'so saying'.) 'So doing' conveys a meaning of 'and while doing that ...' or 'and after doing that ...' It can be omitted without affecting the structure of the sentence. 'Doing so' has the sense of a subject or object phrase and cannot be omitted (though it can be paraphrased).

Examples:

'He agreed that he would take the rubbish out, and so doing, he left the room.'

'She threatened to throw the plate at me, and so doing, she stormed out.'

'"I'll go and find out now." And so saying, he hung up the phone.'

'I advised him to repay the debt, but he said he would not be doing so.' (What did he say he would not do? Repay the debt.)

'You could write her a letter, but doing so will not help your cause.' (Doing what will not help your cause? Writing to her.)

'I think they are wrong, but saying so would only make things worse.' (Saying what will make things worse? That they are wrong.)

Answer 2

"Doing so" refers to completing an action that has been previously mentioned, while "so doing" refers to the action itself. For example, "He closed the door, thus preventing any noise from entering" (doing so) and "He closed the door, preventing any noise from entering" (so doing).