After cartooning for a local newspaper, Blevins became a professional comic book artist in the early 1980s. During that time, Blevins drew Marvel Comics adaptations of films such as The Dark Crystal, Krull, andThe Last Starfighter. Blevins was a guest artist on a number of titles before becoming the regular artist of The Bozz Chronicles, which was published under Marvel's creator-owned Epic Comics imprint.
Blevins first regular job on a superhero comic was on the 1987 revival of Strange Tales. Strange Tales was an anthology that featured two ongoing features produced by two different creative teams — Cloak and Dagger drawn by Blevins, and Doctor Strange.
That same year, Blevins became the regular penciler on New Mutants. Blevins drew the majority of issues from #55 to #83. Blevins later became the regular artist on Sleepwalker.
Blevins then began to work primarily on comic books produced by DC Comics, especially Batman comics.
In 1996, Blevins moved into the field of television animation. He primarily drew storyboards for Warner Brothers-produced cartoons such as Superman, The New Batman/Superman Adventures, Batman Beyond, andthe Justice League. In 1996, Blevins won two Emmy Awards for his storyboard contributions to some of those shows.
Blevins stopped regularly drawing storyboards in 2005. He now does gallery art, primarily oil paintings, and boosts his income with freelance storyboard work.
Blevins's freelance work has appeared in Disney Magazine as well.