Mitchell received a BS (1981, Physics and Applied Mathematics), and an MS (1981, Mathematics) from Carnegie Mellon University, and Ph.D. (1986, Operations Research) from Stanford University (under advisership of Christos Papadimitriou).

Mitchell has served for several years on the Computational Geometry Steering Committee,[2] often as Chair.

[7] He has served on numerous program committees and was co-chair of the PC for the 21st ACM Symposium on Computational Geometry (2005).

Mitchell has been an NSF Presidential Young Investigator, Fulbright Scholar, and a recipient of the President's Award for Excellence in Scholarship and Creative Activities.

He shared the 2010 Gödel Prize with Sanjeev Arora for devising a polynomial-time approximation scheme for the Euclidean travelling salesman problem.