This sentence means: word like '断ち切る' is relevant to きっぱりして(?)(?)
I know that 断ち切る modifies きっぱりする but I don't get the meaning of this sentence.
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Isn't this a word definition in some dictionary?
断ち切るように and きっぱり both mean clearly, unambiguously, decisively, etc. In English you can say clear-cut, too.
I don't think 断ち切るように modifies きっぱりする. This 断ち切るように adverbially modifies 言葉がきっぱりして適切な as a whole.
(lit.) for words to be clear and adequate as if it were sharply cut.
using words clearly and adequately.