이거 = this
가지고 = with
뭘 = what
So, the sum of those is roughly like "What + (Subject + Verb) + with + this?"
The literal meanings could be as follows.
1. 이거 가지고 뭘(해요?) = What should I do with this?
2. 이거 가지고 뭘(할거야?) = What are you gonna do with this?
3. etc
Of course, when you use it this way, you should stress 뭘 like it's the question sentences as they are here.
The honorific (but not so much) form is just "이거 가지고 뭘요?"
But when you say this as the form of an exclamation(?), then you can think of more than two things depending on the context. And in these cases, you could say that "고작" or "겨우" will be attached in front of them implicitly.
1. (고작) 이거 가지고 뭘 (그리 잘난척이야?)
=겨우 이정도로 뭘 그렇게 잘난척이야?
=How can you be so cocky just from this?
2. 이거 가지고 (도대체) 뭘 (어떻게 하란거야?)
=What the heck should I do just with this?
3. (겨우) 이거 가지고 뭘 (그렇게까지 해?)
=Why do you do that much just because of this?
4. etc
Needless to say, you can always use this in a good way too.
5. (겨우) 이거 가지고 뭘(요 / 그렇게까지 절 칭찬해주시나요 ^^;)
=You don't need to praise me that much just for that.
=It was nothing. / Don't mention it. / You are welcome