You can translate no mames literally. Mamar means "to suck," from mama's breast. Word for word, no mames is "don't suck." So much for untranslatable.
The problem is that the literal translation is the least true thing about the phrase. "Don't suck" tells an English speaker nothing about what no mames actually does, which is carry disbelief, shock, delight, or "you have got to be kidding me," with a register that flips entirely depending on your tone and who's in the room.
Here's the proof. In polite company Mexicans don't say no mames; they say no manches. Manchar means "to stain," so the clean version literally means "don't stain." Suck and stain have nothing in common. What the two phrases share is the only thing that matters: the job they do in the conversation. The euphemism keeps the function and throws away the dictionary.
That's the part literal translation can't reach, and it's the part that actually carries meaning. Words are the surface. The meaning lives in function, register, and who's listening. It's also exactly the layer machines still flatten: a model can give you "don't suck" instantly and be perfectly, uselessly correct.