To the best of my knowledge, there never has been any US law which authorizes killing or executing someone simply because of their low intelligence or mental illness.
The arguments have been over cases where people were accused and convicted of serious, even horrific, crimes, but were sufficiently low in intelligence that it was argued that they would not understand why they were being executed, or even could not form the criminal intent required for a valid conviction.
I never saw any news story or advocacy piece, even from the most passionate advocates of preventing such executions, that said or implied that people were being executed just because of low intelligence. Some may have suggested that comparable criminals of higher intelligence were not as likely to be executed. If any publication claimed the people were being executed just because of low intelligence, who were not convicted criminals, it was incorrect, and I would like to known what publication that might have been.
However, there was a time in the US, not so very long ago, when coercive actions were taken against people solely because of their alleged low intelligence. I refer to Buck v. Bell, 274 U.S. 200 (1927) a US Supreme Court case in which the Court held that a state law providing for the compulsory sterilization of the "unfit", including the intellectually disabled, "for the protection and health of the state" did not violate the Due Process clause of the 14th Amendment.
The decision by Justice Oliver Wendell Holmes included the passage:
We have seen more than once that the public welfare may call upon the best citizens for their lives. It would be strange if it could not call upon those who already sap the strength of the State for these lesser sacrifices, often not felt to be such by those concerned, to prevent our being swamped with incompetence. It is better for all the world, if instead of waiting to execute degenerate offspring for crime, or to let them starve for their imbecility, society can prevent those who are manifestly unfit from continuing their kind. The principle that sustains compulsory vaccination is broad enough to cover cutting the Fallopian tubes.
and went on to say:
Three generations of imbeciles are enough.
The Wikipedia article linked above says that Buck's lawyer was a member of the Board of the mental institution that issued the order of sterilization, and may have intentionally done a poor job of arguing the case.
The late Stephen Jay Gould, in his essay "Carrie Buck's Daughter" (published in Natural History, July 1984, reprinted as essay 20 in The Flamingo's Smile, 1987, and available online) wrote:
As scholars and reporters visited Carrie Buck and her sister, what a few experts had known all along became abundantly clear to everyone. Carrie Buck was a woman of obviously normal intelligence. For example, Paul A. Lombardo of the School of Law at the University of Virginia, and a leading scholar of the Buck v. Bell case, wrote in a letter to me:
As for Carrie, when I met her she was reading newspapers daily and joining a more literate friend to assist at regular bouts with the crossword puzzles. She was not a sophisticated woman, and lacked social graces, but mental health professionals who examined her in later life confirmed my impressions that she was neither mentally ill nor retarded.
When we understand why Carrie Buck was committed in January 1924, we can finally comprehend the hidden meaning of her case and its message for us today. The silent key, again and as always, is her daughter Vivian, born on March 28, 1924, and then but an evident bump on her belly. Carrie Buck was one of several illegitimate children borne by her mother, Emma. She grew up with foster parents, J.T. and Alice Dobbs, and continued to live with them, helping out with chores around the house. She was apparently raped by a relative of her foster parents, then blamed for her resultant pregnancy. Almost surely, she was (as they used to say) committed to hide her shame (and her rapist’s identity), not because enlightened science had just discovered her true mental status. In short, she was sent away to have her baby. Her case never was about mental deficiency; it was always a matter of sexual morality and social deviance.
... She [Carrie's daughter Vivian, the crucial "third generation"] was a perfectly normal, quite average student, neither particularly outstanding nor much troubled. In those days before grade inflation, when C mean “good, 81-87” (as defined on her report card) rather than barely scraping by, Vivian Dobbs received A’s and B’s for deportment and C’s for all academic subjects but mathematics (which was always difficult for her, and where she scored D) during her first term in Grade 1A, from September 1930 to January 1931. She improved during her second term in lB, meriting an A in deportment, C in mathematics, and B in all other academic subjects; she was on the honor roll in April 1931
Gould also notes that sterilizations were performed at the same institution, under the same law, until 1972, for a total of over 4,000 cases at that institution alone.
That is what US jurisprudence has in fact done to people alleged to be "feeble-minded".