Saladin personally administered the chop.
That’s a weight off his shoulders.
Conduct so ill comporting with Saladin‘s reputation for chivalry had been earned by Raynald’s own bad behavior.
Crusaders with a view to realpolitik saw that the Kingdom of Jerusalem had to coexist with its Muslim neighbors. Raynald (or Reynald, or Renaud) just preferred killing them.
His raids against Saladin’s caravans when the Crusader state was supposed to be at peace with the Ayyubids precipitated the war that would claim his own head — and, within three months of this date, Jerusalem itself.
The Muslim commander vowed going in to slaughter the notoriously vicious Raynald if he captured him. Here he is making good the threat in the ponderous Ridley Scott epic Kingdom of Heaven:
According to the account (sourced to Wikipedia, such as it is) of Saladin house historian Imad ad-Din al-Isfahani, an eyewitness to the event,
Saladin invited the king [Guy] to sit beside him, and when Arnat [Raynald] entered in his turn, he seated him next to his king and reminded him of his misdeeds. “How many times have you sworn an oath and violated it? How many times have you signed agreements you have never respected?” Raynald answered through a translator: “Kings have always acted thus. I did nothing more.” During this time King Guy was gasping with thirst, his head dangling as though drunk, his face betraying great fright. Saladin spoke reassuring words to him, had cold water brought, and offered it to him. The king drank, then handed what remained to Raynald, who slaked his thirst in turn. The sultan then said to Guy: “You did not ask permission before giving him water. I am therefore not obliged to grant him mercy.” After pronouncing these words, the sultan smiled, mounted his horse, and rode off, leaving the captives in terror. He supervised the return of the troops, and then came back to his tent. He ordered Raynald brought there, then advanced before him, sword in hand, and struck him between the neck and the shoulder-blade. When Raynald fell, he cut off his head and dragged the body by its feet to the king, who began to tremble. Seeing him thus upset, Saladin said to him in a reassuring tone: “This man was killed only because of his maleficence and perfidy.”
The Egyptian classic El Naser Salah el Dine, whose composition and subject matter reflect its production at the acme of Nasser-led Pan-Arabism, noticeably soft-pedals this scene, with Raynald as an over-the-top boor who challenges his captor to a duel and is slain in a fair fight. (Skip to about 35:25 in the clip below to see it, but the whole thing is well worth the watching.)