In doing the Duo. Esperanto Home topic, I came across this sentence about a knife being a tool for cutting. I used tranĉa and was corrected in that it should be tranĉi, which I "thought" was the verb meaning 'to cut'. So am I to assume that "tranĉi" means to cut as well as cutting.? The sentence being...a knife is a tool for cutting.
You can indeed use "cutting" as an adjective, for example saying something has a "cutting edge" (or is "cutting edge").
However, in the sentence you gave, I believe it is a gerund. You can hear it as something similar to "a knife is a tool (for) to cut". In that case, in Esperanto it becomes an (infinitive) verb, and so it would be "Tranĉilo estas ilo por tranĉi."