In 2012, Dr. Grinnell received a Regents' Outstanding Teaching Award. The awards were established by the Board of Regents in 2008 as part of its commitment to the UT System as a place of intellectual exploration and discovery, educational excellence, and unparalleled opportunity. He wrote on the UT System Award website,
In college and graduate school, I was introduced to the idea that science and philosophy were inseparable — scientific discoveries have important implications about philosophical ideas; philosophical ideas have important implications about scientific discoveries. By the time I became a faculty member, I was convinced that philosophy should be a part of graduate science education, and that every student should wonder, 'Why do I believe what I think I know?' That conviction provides the inspiration for my teaching efforts.
In 2017, Grinnell received a Minnie Stevens Piper Professor Award presented each year to 10 Texas college and university teachers for outstanding academic, scientific, and scholarly achievement and for dedication to the teaching profession.
Grinnell is a member of the UT Southwestern Academy of Teachers and was named Distinguished Biomedical Science Educator in 2019. Also in 2019, Grinnell's elective course Introduction to Biomedical Ethics won first place in the UT System Shine Academy Innovations in Health Science Education competition.