Stacchi graduated from California Institute of the Arts with a BFA in Film in 1986.

He then went on to be an Animator and Commercial Director at San Francisco's Colossal Pictures and an effects animator at Industrial Light and Magic on Back to the Future 2 and 3, Hook, The Rocketeer and Ghost, and Henry Selick's James and the Giant Peach.

He was a storyboard artist for Antz, Spirit: Stallion of the Cimarron, Astro Boy, Missing Link, and Del Toro's Pinocchio and was the head of story for ILM's aborted animated feature Frankenstein, and a short film, Work in Progress.

He made his directorial debut as co-director of Sony Pictures Animation's first film Open Season.

He directed the 3D stop-motion animated feature film The Boxtrolls, at Laika.