Extremely disappointed or devastated; can also mean having the insides removed or cleaned out.
From Old English 'gut,' related to 'pouring' or 'channel.' Originally meant the physical removal of insides; the emotional meaning developed because extreme disappointment feels like something inside you is being removed.
The physical meaning (removing organs) came first, but the emotional use is brilliant—when you're 'gutted,' you feel hollowed out, empty inside, which is exactly what physically removing guts would do. It's metaphor that makes perfect sense.
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