Cut is a really terrible example though, because the entire naming of the 'cut' operation isn't intuitive. "Cut" is really "relocate-object-action-first-half" and "paste" is really "relocate-object-action-second-half". We don't have good words for that. The entire relocation object involves program state and that adds some extra complexity.
Cut has a whole heap of connotations that don't relate to the editing "cut" operation. Google suggests incision, wound, to separate into parts, "remove (something) from something larger by using a sharp implement". Editing cut doesn't do any of this.
There is a very specific link in that relocating text /could be/ thought of as snipping it off a page and pasting it somewhere else, except no-one would ever do that when writing seriously. They erase and rewrite.
So the scissors icon links to the word cut, but cut itself is actually a mystery-meat operation where figuring it out is hard for users that aren't already savvy with interfaces. By extension, the scissors icon has no link to the actual operation that the button performs.