He was referring to the execution for "terrorism" Saturday of Nimr al-Nimr, who had been behind anti-government protests among Saudi Arabia's Shiite Muslim minority.
Officials have not said how Nimr was put to death, but beheading is common in the conservative Sunni Muslim kingdom, which has since cut diplomatic ties with predominantly Shiite Iran.
"One does not respond to criticism by cutting off heads," Rouhani said as he welcomed visiting Danish Foreign Minister Kristian Jensen to Tehran.
Human rights groups frequently criticise use of the death penalty in Iran, where hanging is employed.
Rouhani also accused the Middle East's top Sunni Arab power of using the row over Nimr, which led a mob to ransack and set fire to the kingdom's embassy in Tehran, as an excuse to sever ties.
Saudi Arabia's consulate in second city Mashhad was also torched.
"Saudi Arabia cannot cover its crime of having cut off the head of a cleric by cutting relations," he said.
The violence was condemned by Rouhani, and Iran's judiciary has said 50 people involved in the incidents, including ringleaders, have been arrested and will face legal action.
Before Rouhani spoke, a government spokesman, Mohammad Bagher Nobakht, said cutting diplomatic relations would not hurt Iran or damage its development.
Bahrain and Sudan also broke ties with Iran, and a number of other Arab countries have recalled their envoys, in sympathy with Riyadh.
Commerce between Iran and the countries that have severed relations is low, according to official figures released today by economic daily Donaye Eghtesad.
Bilateral trade between Iran and Saudi Arabia reached USD 172.5 million during the first eight months of the Iranian year that began on March 20, 2015.
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