Mohri received bachelor and master of science degrees in chemistry from Hokkaido University in Sapporo and in 1976 received a doctorate in chemistry from Flinders University of South Australia in Adelaide. He served for 10 years on the faculty of Hokkaido University, beginning in 1975, with special interest in the fields of surface physics and chemistry. He was selected in 1985 by the National Space Development Agency (NASDA) of Japan as one of the first three Japanese astronauts. While awaiting a flight assignment, he worked at the Center for Microgravity and Material Research at the University of Alabama, Huntsville, for two years. After his eight-day flight in 1992, on which he assisted in the conduct of 44 experiments in life sciences and materials processing, Mohri became head of the NASDA astronaut office. Mohri entered full astronaut training at the National Aeronautics and Space Administration's Johnson Space Center in Houston in 1996 and flew as a mission specialist aboard the Shuttle Radar Topography Mission in February 2000.

In July 2001 Mohri became the first director of the Museum of Emerging Science and Innovation in Tokyo.