Grammozis was born on July 8, 1978, in Wuppertal, Germany, to Greek parents. He started his football career in 1995 with KFC Uerdingen and has played with Hamburger SV (1999-2000), 1. FC Kaiserslautern (2001-2005) and 1. FC Köln (2006).
In July 2006, Grammozis negotiated with AE Larisa but instead chose to sign with Rot-Weiss Essen. He played for Ergotelis between 2007 and 2008 and spent the 2009 and 2010 seasons in Cyprus with Omonia Nicosia.
Grammozis was capped 8 times for the U21 of Greece.
After his playing days Grammozis was manager of VfL Bochum II and Darmstadt 98 in Germany.