Texas has executed an intellectually disabled prisoner despite a high court ban on putting mentally impaired prisoners to death, the second such violation of constitutional protections to occur in the US this week.

Robert Ladd, 57, died by lethal injection on Thursday evening. Under Texas’s unique – and widely ridiculed – definition of intellectual disability, he was deemed capable of being executed because he did not match the degree of mental impairment depicted in a character in a John Steinbeck novel.

In his final statement Ladd addressed the sister of his victim by name, telling her he was “really, really sorry”.

“I really, really hope and pray you don’t have hatred in your heart,” he said, adding that he didn’t think she could have closure but hoped she could find peace. “A revenge death won’t get you anything,” he said.

Then Ladd told the warden: “Let’s ride.”

As the drug took effect he said: “Stings my arm, man!” He began taking deep breaths, then started snoring, the Associated Press reported. His snores became breaths, each one becoming less pronounced, before he stopped all movement.

He was pronounced dead at 7.02pm, 27 minutes after the drug was administered.

The death of Ladd exposed a flaw in the normally stringent safeguards imposed by the federal courts on the death penalty states. Although the states are generally allowed to set their own standards, the US supreme court has ruled twice on the issue of intellectual disability in order to set the parameters of humane and civilised conduct.

In the rulings – in 2002 and last year – the high court banned executions of people with “mental retardation” on the grounds that they were a form of cruel and unusual punishment prohibited by the eighth amendment. It also said that the death penalty states had to conform to standards set by medical science and not impose their own arbitrary definitions of mental disability.

Yet this week two prisoners who were categorically found to be mentally impaired by numerous medical experts have been put to death. The first was in Georgia where Warren Hill, 54, was judicially killed on Tuesday .

Texas put Ladd to sleep by lethal injection having deemed him not to be sufficiently mentally impaired according to its bizarre criterion for the condition. Under what are known as “Briseno factors”, the state sets out the profile of an individual whom ordinary Texans would agree was intellectually disabled. It points to Lennie Small, the lumbering and childlike character in John Steinbeck’s 1937 novel Of Mice and Men, identifying him as the legal yardstick.

Ladd’s lawyer, Brian Stull of the American Civil Liberties Union, said that his client’s fate should not have depended “on a novella. Instead of sticking to the standards set by science, they refer to a character in Of Mice and Men.”

Ladd was convicted of the 1996 murder of Vicki Ann Garner in east Texas. Previously, he had served 16 years of a 40-year prison sentence for murdering another woman and setting her Dallas apartment on fire, killing her two children.

Stull said that the two executions of mentally impaired prisoners in one week proved that “we are in the midst of a complete systems failure in terms of honouring the constitutional protections the supreme court ordered for intellectually disabled people”.

On Wednesday, the supreme court ordered a stay of execution in three pending cases in Oklahoma as a result of the court’s earlier decision to consider the use of the sedative midazolam in lethal injections. Midazolam has been linked to a spate of recent botched executions in Oklahoma, Arizona, Florida and Ohio.

The review did not touch upon Texas’s procedures, as the state has chosen to use pentobarbital, a barbiturate it is believed to have acquired from a relatively unregulated compounding pharmacy.