The end of 1 Samuel says Saul fell on his own sword. This man says Saul begged him to finish him off, so he did. The Bible gives both accounts.
Mount Gilboa. The Philistines kill Jonathan and his brothers. Saul is badly wounded by archers. His armour-bearer is too afraid to kill him, so Saul falls on his own sword. Saul and his three sons die together that day.“I happened to be on Mount Gilboa,” he replied, “and there was Saul, leaning on his spear, with the chariots and the cavalry closing in on him. When he turned around and saw me, he called out to me, and I answered, ‘Here I am!’ ‘Who are you?’ he asked. So I told him, ‘I am an Amalekite.’ Then he begged me, ‘Stand over me and kill me, for agony has seized me, but my life still lingers.’ So I stood over him and killed him, because I knew that after he had fallen he could not survive. And I took the crown that was on his head and the band that was on his arm, and I have brought them here to my lord.”