I’m puzzled by this expression.  I can see the imagery behind “give me some slack”: a tethered animal is given greater freedom by slackening off the tether, but why “cut”?

Why “cut” in “cut up” or “cut the mustard” or “that doesn’t cut it” or “cut a rug” or “cuts a fine figure”?

Just idiomatic I think.

I agree it doesn’t make sense. It may have to do wth the sense of ‘cut’ as in divide off; one says ‘cut me some cake’ (but don’t cut the cheese) for example. I remember a guy who used ‘cutting’ for shoveling sand or dirt. A little more logical than for ‘slack’. It’s possible that it was common to say ‘cut me some rope’ as an informal way of ‘give me some more’. Good question.

I agree with Foolscap. “Cut” in ‘cut me some cake’ can also mean ‘give me some cake’. You want a little slack? I’ll cut a piece of that slack for you.

(but don’t cut the cheese)

Is there a saying “cut me some rope” that predates “cut me some slack” and means the same thing?

BTW how do you eat cheese without cutting it?

There is “cut me a break” but I can’t find that in OED to ascertain whether it’s older.

BTW how do you eat cheese without cutting it?

“Cut the cheese”

I’m almost sorry you asked. It must be an americanism. Without actually going into detail, let me give a couple of examples. Back in the 70s there was a rather hilariously named organic food brand, “Gathering Winds”, that sold among other things sauerkraut and chile beans. (True story) Then of course there’s a famous housing development near where I live. It’s in a former industrial area overlooking the slough where the factories used to dump their effluent. (One of the companies was an oil refinery founded by Mr. Passe, the Passe Gas Company. “We pass the gas to you” was their motto.) To take homeowners’ minds off the smell and to spruce up the image they wanted a somewhat romantic name and came up with “The Breakwinds”.

Ah, I get it now!

It’s an oldie. You can hear it very briefly in American Graffiti when the Richard Dreyfuss character gets into the car with the Pharaos gang.

Previous discussion: cut me some slack.

And another.

FTR, the person I referred to as using “cut” for shovelling was African American. He was memorable; much like John Henry he could swing a 6 or 8 pound sledge hammer to drive stakes with one hand, at the long end of the handle.