In 1964, while attending Cortez High School in Phoenix, Arizona, Buxton made his debut in a rock band called The Earwigs, comprised of high school students Dennis Dunaway and Vincent Furnier. They were very popular, and changed their name to The Spiders in 1965, and later to The Nazz in 1967. In 1968, to avoid legal entanglements with the Todd Rundgren-led "Nazz", Buxton's band changed their name to Alice Cooper.

Buxton was the co-writer of classic songs like "School's Out", "I'm Eighteen", "Elected," and "10 Minutes Before the Worm." He is credited as lead guitarist on seven albums by the Alice Cooper band, including the chart-topping Billion Dollar Babies, although he didn't actually play much on it due to poor health. Throughout the late '70s and '80s, Buxton maintained a low profile, playing only occasional club gigs with obscure bands like Shrapnel and Virgin.

In the 1990s, Buxton lived on a farm near Clarion, Iowa performing with local artists. A few weeks shy of his 50th birthday, he died of complications from pneumonia at a hospital in Mason City, Iowa. Before his death, the guitarist was able to spend time with his old bandmates; Alice Cooper, Dennis Dunaway, Michael Bruce, and Neal Smith.

In 2003, Rolling Stone magazine named Buxton one of the "100 greatest guitarists of all time."