Polyester, if you've looked up 'clumsy' in the dictionary and found something like this, 'Difficult to handle or use; unwieldy' you could be mistaken for thinking that a rope could be clumsy, but that would not sound natural at all. If that is the sense you were after, you should use 'unwieldy'. If not, follow Matthew's advice.
Given the context of someone throwing you a rope, with the throw being smooth but the aim wrong (so that the catcher had to run and pick it up), 'awkward' might work - but it would sound a bit odd.
It depends what you mean by "work". It would make a kind of sense to me, by analogy with expressions like "there was a guilty sweet-wrapper on the floor" - where the adjective really refers to the person who dropped it.. (Maybe this sort of anthropomorphhism is more common this side of The Pond.)
If you have a question about the English language and would like to ask one of our many English teachers and language experts, please click the button below to let us know: