If you're one of the six people who haven't seen George Miller's masterpiece MM:FR, what's up with that? They don't have movie theaters where you're from? If you have seen, you know that the real star of the film is not Max, but Imperator Furiosa. Played brilliantly by Charlize Theron, Furiosa, daughter of Mary Jabassa (one of the Vuvalini of Many Mothers) was born in The Green Place. She was kidnapped along with her mother by Immortan Joe. While they don't address how Furiosa lost her left arm, I'm going to guess that Immortan Joe had it removed.
Furiosa escaped Immortan Joe's tyranny as Imperator Furiosa - one of Immortan Joe's most trusted warriors - while driving the War Rig she uses to get back to The Green Place. Unfortunately after meeting the Vuvalini she learns that The Green Place does not exist anymore and she's forced to find another solution with help of Max.
if you haven't seen this film, yet for god sakes get your ass the theatre. If you have, it's even better the second and third times.