I agree with Paul, too. It's not a question of having a literal or any other meaning - the sentence just doesn't make sense.
You can only 'do up' things that have fixed fastenings, like jackets with zips or shirts with buttons. 'Do up' is not a synonym for 'shut'. You can't 'do up' something that you can't fasten - you can close/shut a door, for example, but you can't do it up.
Similarly, you can say 'shut your mouth', but it's not possible to replace 'shut' with 'do up'.