Incisively is how someone speaks, writes, or thinks when they are being incisive: clearly, sharply, and on the point, without extra fog. If a teacher comments incisively on an essay, she puts her finger on the real weakness in a few words. If a report argues incisively, it does not dance around the problem. It is the adverb form, so it tells you about the manner. Formal, complimentary, a little bookish — the same register as incisive itself. You would not usually use it for the way someone cuts bread.