While the origins of the weapon are not known, It was first seen on the hand of Skurge the Executioner who used it to cut portals, shatter worlds, control fire and ice and summon great hurricane winds. It's implied such powers came from the Amora the Enchantress who cast spells on the axe, although it is possible that a greater enchantment existed within it as well.
After the Executioner's death the axe fell to Earth and was used by mortals and the magic would surge through their bodies transforming them into monstrous creature know as Bloodaxe. Thunderstrike fought Bloodaxe several times before finally killing him but unknown to Thunderstrike the axe was cursed and anyone who wielded it eventually fell prey to its savage power, twisting the minds of those who held it. During it possessing Thunderstrike's mind, he sought to battle more powerful villains among them Seth the Serpent God. It was only after he defeated the god that he saw what the axe was doing to him and sought to end his life and take the weapon with him.
Sometime later however, the Bloodaxe of Skurge ended up in the possession of Mistress Hela, and after the death of Odin, she realized that she would have to act quickly and use the great power of the axe to take the life of Thor before the Odin Force became his to command. She used her own power, as well as that of the axe, to create a "clone" of Skurge the Executioner, sending him to Earth to draw out the Odinson. The plan failed, as the awesome power of Odin had already begun to grow inside Thor. Upon confronting Hela in Hel, Thor brought the defeated "Skurge" before her, demonstrating Odin's power by stripping away the appearance of Skurge, revealing it to be one of Hela's many Cyphers. Realizing that Thor was now beyond her reach, and that he was her master, Hela submissively obeyed his final warning to never again interfere with him in any way, and Thor took the Bloodaxe of Skurge so it's power could never be exploited by anyone again.
During the future in which Thor would begin to take control of planet Earth called 'Thor- Lord of Earth' a mysterious god killer by the name of Desak sought out to kill the God of Thunder after learning from the time traveler named Zarrko that Thor had inherited his fathers vast power known as the Odin Force, as well as what the future would await Earth if Desak did not kill the son of Odin. But despite Thor's best efforts, not even Mjolnir nor his father's power could stop Desak's vicious assault upon him. It was only the delivery and power of the Bloodaxe of Skurge the Executioner by Thialfi, that Thor was able to finally strike down the slayer of gods. if not for the Bloodaxe, Thor would have been beheaded by Desak.
For a short time after slaying Desak, Thor carried the Bloodaxe beside him alongside Mjolnir, but when Perrikus of the Dark Gods attempted to invade Asgard alongside Adva, Thor had reached a point where he finally lost all patience with him, viciously using the axe to slice Perrikus' arm clean off. It was at that moment that a stunned Thor stared in shock at the Bloodaxe, realizing that it was trying to control his thoughts. Thor was able to resist the awesome power of the savage weapon, and used the Odin Force to destroy it completely, stating that it's days of victimization had come to an end.