Smith will not be directly replaced, with the team instead introducing a new technical committee to oversee all technical and operational aspects of activities both on and off track.
The new structure will be filled by John Iley, Jody Egginton and Gerry Hughes, who will each take responsibility for specific areas of the team, and will collectively report to team principal Cyril Abiteboul.
Iley joined the team in 2012 and worked most recently as performance director, but will now serve as head of performance, with increased involvement in the aerodynamics and performance of the car. Egginton, previously deputy technical director, is now the team's head of design and manufacturing, and as such will oversee every part of the design process, from early concept drawings to rig testing and manufacturing. Hughes, who joined as chief engineer earlier this year, meanwhile steps up to head of track operations.
Abiteboul said the reshuffle had created a more streamlined and efficient structure, while also paying tribute to the departing Mark Smith.
"First I would like to thank Mark for his time and dedication to the development of our team since he first joined in 2011," he said. "We and Mark part company on good terms and with our best wishes for the future.
"It was obviously a tough decision to see someone of Mark's calibre go, but we have identified the need to restructure as a key aspect of increasing our on-track performance and forming a new technical committee composed of John, Jody and Gerry will allow us to do exactly that.
"After investing last year in our new factory, and over the winter in aerodynamic development capacity, the new structure gives three specialists we are lucky to have with us the opportunity to use their experience, passion and dedication to help us progress.
"We are not happy with our current performance levels and John, Jody and Gerry, with my full support and that of our shareholders, staff and partners, are the right people to help take us forward."
Caterham currently lie 11th in this year's constructors' championship, with Kamui Kobayashi's 13th place in Malaysia the team's best result of the year.
They have not scored a point since joining the F1 grid ahead of the 2010 season.