They beheaded him when their ransom demands were not met. This is all according to Islamic law. Here is a salient passage on this issue from a Shafi’i manual of Islamic law:
When an adult male is taken captive, the caliph considers the interests … (of Islam and the Muslims) and decides between the prisoner’s death, slavery, release without paying anything, or ransoming himself in exchange for money or for a Muslim captive held by the enemy. (Umdat al-Salik (Reliance of the Traveller) o9.14)
A revered Islamic jurist, Al-Mawardi, agrees with Reliance of the Traveller:
As for the captives, the amir has the choice of taking the most beneficial action of four possibilities: the first, to put them to death by cutting their necks; the second, to enslave them and apply the laws of slavery regarding their sale or manumission; the third, to ransom them in exchange for goods or prisoners; and fourth, to show favor to them and pardon them. (Al-Ahkam As-Sultaniyyah (The Laws of Islamic Governance), 4.5)
“‘Vicious and brutal’: A second Canadian man is beheaded by Islamist militants in the Philippines,” by Ben Guarino, Washington Post, June 14, 2016:
A small group of Islamist militants in the Philippines, known as Abu Sayyaf, has beheaded a second Canadian hostage in two months, authorities said Tuesday.
“We strongly condemn the brutal and senseless murder of Mr. Robert Hall, a Canadian national, after being held captive by the Abu Sayyaf group in Sulu for the past nine months,” Herminio Coloma, a representative for the Philippines President Benigno Aquino, said in a statement, according to AFP. A head believed to belong to Hall, 58, was found Monday on an island near an Abu Sayyaf outpost.
In April, the same group decapitated Canadian John Ridsdel, a 68-year-old businessman. Gunmen had kidnapped Ridsdel and Hall, along with Hall’s Filipina partner Marites Flor and a resort manager from Norway named Kjartan Sekkingstad, from the island of Samal in September….
Abu Sayyaf has a decades-long history of taking hostages and demanding ransoms, which both the Canadian and Philippine governments oppose paying. AFP reports that Abu Sayyaf murdered Hall when a $6.5 million ransom demand was not met….