After attending the University of California, Santa Cruz for fine art and studying at Art Center College of Design as an illustration major, Liu got his first job in comic books drawing for Image Comics. In 1996, he moved to animation, directing Roughnecks: Starship Troopers Chronicles and Godzilla: The Series for Sony Animation. He later went to Sony Computer Entertainment of America to design characters for PlayStation, then came back to animation, winning a Daytime Emmy Award for his work on The Batman series in 2006.
Liu has since worked on many animated films for Marvel Entertainment and Warner Bros. Animation, including All-Star Superman, Superman/Batman: Public Enemies, Hulk Vs, Planet Hulk, Thor: Son of Asgard, and co-directing with Lauren Montgomery on Justice League: Crisis on Two Earths and Batman:Year One. Liu was also the primary character designer for Superman/Batman: Apocalypse. In 2010, Liu moved back to television, directing Green Lantern: The Animated Series with Bruce Timm, and Beware the Batman with Glen Murakami.
He then directed the animated film Justice League: Gods and Monsters and its companion series Justice League: Gods and Monsters Chronicles written by Bruce Timm. He has directed the 2016 animated film Justice League vs. Teen Titans, the animated adaptation of Batman: The Killing Joke, the 2017 animated films Teen Titans: The Judas Contract and Batman and Harley Quinn, and the 2018 animated adaptation of Gotham by Gaslight.