Hermes is a mythological figure and therefore can't have died, since he never actually lived.
I'm unaware of any myth featuring the death of Hermes.
(There have been a number of actual people named Hermes; if you mean one of them, you'll need to provide additional details.)
Hermes never died in Greek mythology.
Ad Hermes died in 2002.
Hermes Lima died in 1978.
Hermes Grillo died in 2006.
Georg Hermes died in 1831.
Andreas Hermes died in 1964.
Saint Hermes died in 120.
Gertrude Hermes died in 1983.
Hermes in Greek mythology never died.
Hermes is a Greek god, so he never died.
Hermes Pan - choreographer - died in 1990.
Johann Gustav Hermes died in 1912.