After earning his undergraduate degree from the University of Madrid, Spain, Mendez came to the U.S. to continue his education in physics, earning a Ph.D. from the Massachusetts Institute of Technology in 1979. He then took a postdoctoral position at the IBM T. J. Watson Research Center in Yorktown Heights, New York, where he became a research staff member and eventually a member of the strategic planning group and a line manager. He joined Stony Brook University in 1995 as a physics professor, and in 2004 he became Director of the Undergraduate Program in the Department of Physics and Astronomy.
Mendez's research at IBM involved finding ways to make faster transistors and computer chips, as well as more efficient lasers. Currently, he is studying, among other materials, carbon nanotubes, cylindrical carbon molecules with novel properties that may enhance future electronic and optical devices. A Fellow of the American Physical Society, Mendez has received several awards for his significant scientific contributions, including the 1998 Prince of Asturias Prize and the 2000 Fujitsu Quantum Device International Award.