「いくら + (Person) + でも + Negative expression」
is a common and important sentence pattern. It being Japanese, however, the negative expression is often left unsaid. The non-sentence in question is a stereotypical example of this phenomenon.
What is left unsaid here (and instead "expressed" with 「・・・」) would surely be a negative phrase like 「しない」、「しないよ」、「しないさ」, etc.
"However (adjective that fits the context) (the person) may be, he would not do ~~~."
is the meaning of this sentence pattern. To apply this to your "non-sentence", one would come up with a translation like:
"However evil I may be, I am no ogre and I would not go so far as to throw out an album."
I just selected the adjective "evil" and the phrase "would not" for the sake of translation. Clearly, those are not found in the original.
The key is to know what is left unsaid; otherwise, you will not be able to translate something like this into English or other languages.