The meaning and etymology of "cut to the heart"

What part of the bible did you find that in, and which translation (e.g. ESV, NASB, NIV, etc.)?

The modern use of that phrase means "get to the core" or as you said "the crux" since the heart represents the center.

Maybe this will help: the "heart" in the middle ages sometimes meant "stomach" or vise versa, since it was believed all man's emotions arise from the stomach. The "heart of man" means more than the organ that pumps blood; it is the metaphysical collection of a man's feelings and or being.

I have a feeling that in the bible, that could be much more literal. To cut into the blood-pumper, as it were.

Acts 2:37—“When the people heard this, they were cut to the heart and said to Peter and the other apostles, “Brothers, what shall we do?”

In Acts 1:4-5 After his resurrection Jesus told his disciples: “On one occasion, while he was eating with them, he gave them this command: “Do not leave Jerusalem, but wait for the gift my Father promised, which you have heard me speak about. For John baptized with water, but in a few days you will be baptized with the Holy Spirit.”. After this occurred, what we know as the Day of Pentecost, the disciples began to speak in unknown tongues, yet everyone understood what they were saying. Some, even though it was only about 9:00 am, thought they were drunk.

In Acts 2:14 Peter explains to the crowd what’s going on. Quoting Joel 2:28-32 he reproves the crowd bringing clarity and truth to the false accusations: “Let me explain this to you; listen carefully..this is what was spoke by the prophet Joel I will pour out my Spirit on all…Your sons and daughters will prophesy, your young men will see visions, your old men will dream dreams. Even on my servants, both men and women, I will pour out my Spirit in those days, and they will prophesy…”

He goes on to explain how "Jesus of Nazareth was a man accredited by God to you by miracles, wonders and signs, which God did among you through him," and that he "was handed over"....put to death on the cross, "But God raised him from the dead..". Peter furthermore briefly recounted Israel's history and how Jesus surely was the Son of God and Messiah they had hoped for. Upon hearing this truth, then, as referenced in the comments above, (The Book of Acts, chapter 2) "When the people heard this, they were CUT TO THE HEART and said to Peter and the other apostles, “Brothers, what shall we do?” Peter replied, “Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit. The promise is for you and your children and for all who are far off—for all whom the Lord our God will call.”

I believe what "cut to the heart" means then is, what they knew, thought to be true, better yet, what was held dear or close to the heart, was not true. Or at least is no longer true because of the new information given to them: the truth of salvation through Jesus Christ and the forgiveness of sins.

[That] cut to the heart of the larger story I was investigating.

In the sense of the meaning that you are looking for (rather than the Biblical reference), it is important to understand that the phrase is divided:

{[Cut] [to the heart]} {of the subject/matter [in hand]}

In this sense "cut" is, to a degree, a verb of motion implying swiftness of movement:

OED

Cut 18.a. transitive. To pass sharply through, cleave (the air, the water).

a1571 W. Haddon in A. Fleming Panoplie Epist. (1576) 423 Shippes..cut the waves as they are furthered with a merrie winde.

1596 E. Spenser Hymne Heauenly Loue in Fowre Hymnes 69 With nimble wings to cut the skies.

And hence:

19 b. To move sharply, to run rapidly. With various adverbs and prepositions.

1797 B. Hawkins Lett. (1916) 126 He was driving a wagon at the time he was taken, and they cut out and took the horses with him.

1949 ‘M. Innes’ Journeying Boy ii. 25 ‘And now you'd better cut along.’ Captain Cox was a great believer in the moral effects of abrupt dismissals on the young.

Meaning 18a and 19b above create an apt image for "cut to the heart of X" - as it carries both the meaning of slice efficiently with a sharp instrument and implies a swift and decisive action.

To - preposition = as far as

The heart: -

20. With reference to non-material things: the vital, essential, significant, or operative part; the essence or core (of something).

1603 W. Shakespeare Hamlet sig. D3 Our deere cosin Hamlet Hath lost the very heart of all his sence.

1956 R. A. Horn Groups & Constit. ii. 30 Let us cut to the heart of the matter as quickly as we can. We must begin by asking what is the purpose.

1990 Parenting Feb. 38/2 Kids really get to the heart of spelling..when they're engaged in spontaneous writing.

Thus we have a simple combination of words, readily understandable, although mainly figurative, and, as such, a "first mention" is difficult to find as it is not remarkable.

[That] cut to the heart of the larger story I was investigating. = which address directly the essential part of the more complex set of circumstances that I was investigating,