The Malaysian-owned team, who have struggled to make any impression this season and are last in the standings after four races, said in a statement that Smith had left with immediate effect.
"A new Technical Committee has been formed to oversee all technical and operational aspects of the team’s activities on and off track," it added.
"John Iley, Jody Egginton and Gerry Hughes will now each take responsibility for specific areas of the team’s operational activities."
Smith joined Caterham, a team that has yet to score a point in Formula One, in 2011 and took over the technical department from Mike Gascoyne in 2012.
Formula One underwent huge technical changes over the European winter, with a new V6 turbo hybrid power unit replacing the old V8s and revised aerodynamic regulations.
Smith and his design department were under added pressure to deliver results with team owner Tony Fernandes saying before the season started that he could walk away from the sport unless Caterham showed significant improvement.
"If we are at the back, I don't think we're going to carry on," the Malaysian entrepreneur warned in January.
The big step has not happened, with the team's engine provider Renault also suffering teething problems with their power unit that limited running in pre-season testing.
Caterham's drivers are experienced Japanese Kamui Kobayashi and Swedish rookie Marcus Ericsson.
(Editing by John O'Brien)
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