Although widely used by a great many speakers, an expression that makes me cringe is “heart-wrenching.”
Gut-wrenching is fine. Guts twist, both literally and figuratively. And in the bad old days people had their innards pulled out as a form of torture and execution, hence the verb to disembowel and the expression to draw and quarter.
To me, something described as “gut-wrenching” is frightening, the way it’s used in this reader’s comment:
In a mystery the reader is trying to figure out what is going on and the puzzle is more of a brain teaser, but not a gut-wrenching life and death struggle.
“Heart-wrenching,” on the other hand, always strikes my ears as mistake for heart-rending.
I suppose that an argument could be made for either heart-rending or “heart-wrenching,” but it seems to me that when someone says, “The sight of the displaced earthquake victims was heart-rending,” the emotion felt is probably more gentle than the violent word wrench would suggest.
wrench: trans. To twist or turn (a thing) forcibly or with effort; to jerk or pull with a violent twist
A strong argument against “heart-wrenching” is that neither the OED nor Merriam-Webster includes it, while both the British and American dictionaries have entries for heart-rending/heartrending.
heart-rending: That rends the heart; terribly distressing. So heart-rending vbl. n., terrible distress, pangs of anguish; ￼heart-rendingly adv.
heartrending: causing intense grief, anguish, or pain
I suggest reserving wrenching attached to gut for things that cause fear, and rending with heart to describe emotional pain caused by the sight of something truly piteous.