In English you could say
Can you give this to your mother? Sorry, I mean your sister?
The listener can then understand that they are to give the item to their mother, not their sister.
In Korean, how can you make it clear that something you are saying is meant as a correction to something you just said?
You could use "... 말고 ...":
이거 어머니에게 가져다 드릴래? (아니) (그러니까) (내 말은) 어머니 말고 네 동생.
As mentioned in the comments above, several phrases such as 아니/그러니까/내 말은 can also used to mean "I mean."
However, they all have other uses, so they can be ambiguous.
그러니까/내 말은 can be used where you simply explain your word again. For example:
그러니까 내 말은 어차피 다섯 시까지 못 끝낼 테니 그만두자는 거지.
= What I mean is, we'd better quit now as it's clear we won't finish it by 5.
아니 obviously has a zillion other uses. For example:
이 옷 괜찮아 보여요? 아니 내가 입겠다는 게 아니라.
= Does this garment look good? No, I don't mean I'm gonna wear it...
So, I would recommend "아니 그러니까" or "아니 내 말은", although they feel a bit verbose. (Even they can be used for something other than "I mean", but I feel they're more likely to be understood as "I mean".) To recap:
이거 어머니에게 가져다 드릴래? 아니 (그러니까/내 말은) 어머니 말고 네 동생.
You can even say all three at once ("아니 그러니까 내 말은") though that may sound too talkative (sort of like "Err, no, I mean...").
If you are aiming for brevity, I think this could work:
이거 어머니에게 가져다 드릴래? 아, 어머니 말고 네 동생.
("아" is commonly used to mean something like "Oh I just realized...")
