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I can't find it, but I think this is tropable — you see it all the time.
You'll often see it in A Boy and His X plots where the wild animal is captured and panics when the Boy approaches to cut it free (The Rescuers Down Under, How To Train Your Dragon)
There's also a similar thing where the tied hero's enemy cuts the rope by accident. It often popped up in Kim Possible (and kid's shows in general), also I vaguely remember seeing it in Star Wars.
Is there a trope where a tied character is approached by someone with a knife, leading the hero - and, by extension, the audience - to believe they want to kill him, when actually they just want to cut the rope? I remember seeing it in Dexter's Lab (the episode with La Chupacabra) as a kid, and there must've been many more, because when it happened in Avatar it felt cheap and overused.