His father, Graziano Cavalera, was an employee of the Italian Consulate in São Paulo and died at 40 years of age and is buried in Belo Horizonte; Cavalera was nine when his father died. Cavalera's family was in a state of financial crisis and family turbulence when he formed Sepultura with his younger brother Igor.
In the early 1990s, he relocated to Phoenix, Arizona. He did not begin to make spiritual-music until after he quit Sepultura. His earlier lyrics for Soulfly were influenced by religion and spirituality, though he is critical of religion. His later albums, starting with Dark Ages, began to incorporate lyrical themes of violence, warfare, anger and hatred. His albums have all been dedicated to God, and he has often been depicted by the press as a man of religion, especially in the United States, something that Cavalera himself says he does not understand:
I do hate a lot of 'religion,' but people like Christ – yeah they inspire me. I mean if you look at Christ, He was hanging around with the lowlifes, prostitutes and the losers you know, not going around with those high society motherfuckers you see trying to sell Jesus today!
When asked in an interview whether he was a Christian and whether Soulfly was a Christian band, he said:
No. I mean, if I was a Christian I would wear all these different kinds of omens. Because Christian people are so close-minded. A priest would not accept that. So I don't like the concept of Christianity in terms of being so close-minded. It is the same with music. Sometimes I compare preachers to close-minded musicians or close-minded listeners, who only like one kind of music. Some preachers are the same. And they don't tolerate Hindus, Buddhists or whatever. Only them. It's bullshit. So Soulfly is not a Christian band at all. Very much opposite. But we are very spiritual. Spiritual has nothing to do with Christianity anyway. It has been here since the beginning of time.
In another interview, he was asked about the Varg Vikernes church burnings. He quoted, "I support church burnings 100 percent, but why don't we just burn everything. Mosques, temples, all religious buildings." However, he later claimed his views changed about the church burnings and called them "too violent." He has stated that he does believe in God, "But it might be different than the God the preacher preaches about."
Of enduring influence to his music, is the untimely death of his stepson, Dana Wells, who was killed after the release of Roots in 1996. The songs "Bleed," "First Commandment," "Pain," "Tree of Pain" and "Revengeance" are tributes to Wells, as well as Deftones' song "Headup," in which Cavalera featured and co-wrote. He reunited with his brother Igor, in their band Cavalera Conspiracy, and wrote and performed on Soulfly's Conquer, released in 2008. In November 2011, Cavalera announced that he is working on an autobiography, for publication in 2013: his co-writer is the British author Joel McIver and the book's foreword has been written by Dave Grohl. During an interview with Metal Shock Finland, Andreas Kisser described Max's autobiography as science fiction.
Cavalera lives in Phoenix, Arizona with his wife Gloria and his five children, Zyon (b. January 19, 1993), Igor (b. November 11, 1994), Richie (b. February 3, 1989), Jason (b. November 15, 1997), and Roxanne—Richie (b. March 20, 1986), the eldest, was adopted by Cavalera. Zyon, Igor and Richie have all collaborated with Cavalera in his various projects. The three sons are also active in music, with Richie fronting Incite and Igor and Zyon performing in Lody Kong. In 2012 and 2013, Zyon toured with Soulfly after David Kinkade's retirement, and now he is a regular member as drummer. Igor joined Soulfly in 2015 after Tony Campos left the band.
Cavalera has collaborated with many different artists while in Sepultura and Soulfly. In 2003 he joined forces with former Nirvana drummer and Foo Fighters' frontman Dave Grohl to produce "Red War" for the self-titled release of Dave Grohl's metal project, Probot.
Chino Moreno (Deftones) – guest vocalist on "Pain" from the album Primitive by Soulfly and also "First Commandment" on Soulfly's debut self-titled release; Max performed guest vocals on the Deftones song "Headup" from the album Around the Fur