Duffey attended Bellaire High School in Bellaire, Texas. He then enrolled at Rice University to play college baseball for the Rice Owls baseball team. He was named Most Valuable Player of the 2011 Conference USA Baseball Tournament. After the 2011 season, he played collegiate summer baseball with the Falmouth Commodores of the Cape Cod Baseball League. In May 2012, he was named the Conference USA pitcher of the week.
Duffey's mother, Shanna, died in 2012 after complications from breast cancer led to a blood clot. His father, Tim Duffey, and brother, Travis, both reside in Houston. Tyler married his high school sweetheart, Sarah Hutchins, on December 19, 2015.