Stevenson worked as a story artist on the feature films The Great Muppet Caper, The Dark Crystal, Labyrinth and Little Shop of Horrors and as a character designer and story artist on shows and films like The Dreamstone, Count Duckula, Back to the Future: The Animated Series, The Twisted Tales of Felix the Cat, two of the Fox Tales specials and FernGully 2: The Magical Rescue.

He also worked as an art director on Back to the Future: The Animated Series and a puppeteer on James & the Giant Peach and Motion Capture Performer on The Moxy Pirate Show.

[2] In 2011-12, Stevenson directed a six-minute animated short film for The Coca-Cola Company produced by Ridley and Tony Scott called The Polar Bears.

[3] Since 2012, Stevenson has been directing for Rocket Pictures the sequel of Gnomeo & Juliet, titled Sherlock Gnomes, The film was released on 23 March 2018 to negative reception.

[4][5] Stevenson was originally set to work as director for an upcoming film based on the character created by Mattel, He-Man and the Masters of the Universe.