What is the meaning of ‘cut to the heart’

Cut to the heart Bible verses:
Ac 5:33 When they heard that, they were cut to the heart, and took counsel to slay them.
Ac 7:54 When they heard these things, they were cut to the heart, and they gnashed on him with their teeth. (KJV)

cut to the heart, etc. Literally. ‘they were sawn through (excessively irritated), and were consulting to slay them.’ But they were stopped by Gamaliel’s prudence. Annotated Bible Notes

They were cut to the heart. The word used here properly denotes to cut with a saw; and as applied to the mind, it means, to be agitated with rage and indignation, as if wrath should seize upon the mind as a saw does upon wood, and tear it violently, or agitate it severely. Albert Barnes

Cut to the heart. Lit. sawn through, or in two. To be enraged, which is indicated by the gnashing of teeth. Brethren’s NT Commentary

they were cut to the heart, At this indeed we need not be surprised: for what is so cutting as a true charge of guilt; and what so bitter as to have such a charge brought, when persons cannot answer it? Dr. S. Clarke.

Cut to the heart; enraged, filled with wrath. Chap Ac 7:54. When the exhibition of truth torments men, it is evident that they must experience a great change, or their torment will be eternal; for Jehovah is a God of truth, and the progress of his government will be developing and illustrating the truth for ever. Family Bible Notes

They were cut to the heart; they grinned with their teeth, visibly showing the rage and fury that was within them, by which they were as sawn and divided asunder; malice and rage being a grievous torment to the cruel and malicious, Matthew Poole’s Commentary

Cut to the heart. Convulsed with rage, not sorrow. People’s N.T. Commentary