He cut off a slice of meat.
Form my understanding, 切り取る refers specifically to cutting something off something else, as in an amputation, or severing a slice of an object from a larger object. Whereas, 切る encompasses a wider range of meaning, but can have the same connotation as 切り取る depending on the context. Is this accurate?
We use 切り取る as in “cutting a slice of an object from a larger object”. But we don’t so often say it for an amputation. Maybe 切除する (pron. せつじょする) is a better and much more common expression for an amputation of legs, skins, tissues and other internal organs. The smaller part amputated from the larger chunk is a useless/disposable object. The Kanji 除 means “to remove”, so 切除する is the right word for amputation.
肉を一切れ切り取った is most likely to be interpreted as "to slice a piece of meat from the chunk of ham or from the chunk of Doner Kebab. Unlike 切除する, the slice of meat by 切り取る is still useful.
切り取る is also used in different context like this:
その新聞記者は、首相の発言の一部を切り取り、曲解して報じた。= The newspaper journalist partially quoted from the Prime Minister’s speech and delivered it to the public in a misleading way.