It doesn't make sense to judge an ancient figure like Alexander the Great by modern standards, but there's no doubt that he could be extremely ruthless under certain circumstances. For example, when his Macedonian troops staged a second mutiny at Opis in Babylon (324 BC) after their earlier, successful mutiny in India, Alexander "confronted their contumacious [rebellious] demands for repatriation with summary executions and a devastating threat to man his army exclusively from Persians," according to the Oxford Classical Dictionary (OCD, 3rd ed. revised).
Alexander and his snake-handling mother, Olympias, may have been behind the assassination of his father, Philip II of Macedon, but Philip's death remains one of those ancient murder mysteries which may never be solved. Whatever the case, "Alexander was proclaimed king against a background of dynastic intrigue, in which his rivals ... were eliminated. A show of force in southern Greece saw him acknowledged Philip's successor ... and in 335, [when the Thebans rebelled], he destroyed the city and enslaved the survivors." (OCD)
Alexander was more interested in creating a new empire than in butchering his enemies but he was responsible for several massacres, most of them in response to stubborn resistance. For instance, when the Macedonians finally defeated the city of Tyre after a long siege, "[s]ix thousand Tyrians were slaughtered ... and another 2,000 crucified on the beach. A further 30,000 were sold into slavery," according to the Ancient History Encyclopedia. (These figures are probably exaggerated).
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Alexander could be just as ruthless when dealing with rebellion in his own court. For example, "he isolated and struck down Parmenion because of his resistance to imperial expansion, and the adolescent pages, who seriously threatened his life for reasons which are obscure (but probably based on empathy to the new absolutism), were tortured and stoned to death." (OCD)
Note: Parmenion, one of Alexander's most trusted generals, may have simply been murdered to prevent his taking revenge for the execution of his son, Philotas, for treason.
To Alexander, "insubordination was as intolerable as conspiracy," according to the OCD. "Alexander's return to the west in 325/4 witnessed a spate of executions of [puppet] satraps who had exceeded their authority or arrogated power."
Alexander's homicidal behavior sounds grim, true, but it wasn't really all that unusual. He was capable of extreme violence under certain circumstances, but he wasn't Ramsay Bolton. Alexander's use of violence was always calculated. There was nothing mindless or sadistic about it. Executing his internal enemies was necessary to maintain his power and, in some cases, to protect his own life; and massacring the populations of cities that refused to submit was standard operating procedure in the ancient world. Maybe the Dali Lama wouldn't approve, but as a practical matter harsh measures were required to send a message to other cities that might be thinking about resistance.
Photoshop reconstruction based on a bust by the 4th century BC Greek sculptor Lysippos. His depictions of Alexander are thought to be the most accurate, but the various details of Alexander's general appearance (hair color, etc) vary from source to source. He was said to have one blue and one brown eye by more than one source, however - a detail captured in this reconstruction.
Alexander was ruthless but was he "one of the most ruthless kings in history?" Not by a long shot. I wouldn't call him moderate by any means, but he was nothing compared to Vlad the Impaler, for instance, or the bloodthirsty rulers of ancient Assyria who had a well-deserved reputation for cruelty and violence.
All things considered, Alexander showed a surprising amount of tolerance and diplomacy in his conquests. He wasn't a liberal, though. He didn't live in Berkeley or Portland. Like all rulers throughout history, he had to use violence to maintain order and some of the things he did like executing corrupt politicians are practices that we would do well to emulate today.