Which is the correct sentence?

1. Do you mind if I ask you what do you write for a living?

2. Do you mind if I ask what you write for a living?

Both are correct, Ms Tan. The normal neutral is #2, without the second 'do' as it's not needed to mark a question, the first 'do' does that.

But we do sometimes use the style in #1 just as we sometimes use 'do' with a verb as I've done here with 'do' and 'use'.

Number 1 is kinda like this;

Do you mind if I ask you ... what do you write for a living?

Thanks, JTT.