The Cassell Dictionary of Slang throws some light on hack (with twelve meanings for "hack" before the derived phrases!).
"Hacked off," they say, comes from the C19th slang verb "hack", to annoy. By the 1930s "hacked off" meant very angry. Between the late C19th and 1910s, "hacked off" in American slang usage meant exhausted.
"Hack it," they say, comes from the sense of the standard verb "hack," to cut through, via a slang use of "hack" from the 1910s, to accomplish something. They date the phrase "hack it" as "C20th".
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