Meaning of "her cutting words to him"?

Hello everyone. I am reading a novel, and I came across this expression. Could you please let me know its meaning?

I was, I recalled, sitting exactly where the lanky young man had been standing after inadvertently sharing the bathroom with Clara. I had enjoyed her cutting words to him. Even he was far better off than I was right now. I looked over to what had been our table. They had already snuffed out the candles in that corner. The whole place reminded me of an emptied theater when management allows you to go back to retrieve the small umbrella left under your seat—but all the actors, from King Lear to Lady Windermere to the cleanup crew, have gone home already, including the underpaid mopping crew who’s already taken the subway and is on its way to the outer reaches of town, counting the minutes before each man can sit to eat the food his good wife has kept warm for him.

- André Aciman, Eight White Nights, Fourth Night

This is a novel published in the United States of America in 2010. This novel is narrated by the nameless male protagonist who meets Clara at a Christmas party in Manhattan. Three nights after the party, after walking Clara home from a bar, the protagonist returns to the bar and is now remembering his memories with her.

In this part, I wonder what the underlined expression means.

My first guess was that "cut" here is a verb, and it means "talk" like the following meaning in the OED:

†36. Thieves' cant. To speak, talk, say. (transitive and intransitive.) Obsolete.

1815 W. Scott Guy Mannering II. 101 Meg..has some queer ways, and often cuts queer words.

But then I noticed that it is an archaic meaning, so I became confused.

In case this might be helpful, "cutting words" appears again here in this sentence which appears later in Fifth Night:

You’re breaking my heart, Clara, and these are cruel and cutting words that cause heartache, and rupture of blood vessels.

Thank you very much for your help.