He began his football career in 1984 with local side TuS Neviges in the Velbert neighborhood district.
Grammozis spent two years with Hamburger SV, contributing to a third-place 1999–2000 Bundesliga finish and subsequent qualification to the Champions League.
However, he did not manage to permanently assert himself as a regular, and in addition to the arrival of quality players, Grammozis moved to Kaiserslautern in 2000.
In June 2007 Grammozis left Germany and moved to Super League Greece side Ergotelis, signing a one-year contract with an option for another year.
After a successful 2007–08 season with Ergotelis in which he played in 23 games and scored once,[4] the club opted to extend his contract.
However, after falling out with coach Nikos Karageorgiou in November 2008, Grammozis was transferred out to Cypriot First Division side Omonia Nicosia in December for a reported €150,000.
In January 2011, Grammozis returned to the Super League Greece and joined newly promoted side Kerkyra.
On 25 January 2014, Grammozis was hired as assistant to head coach Thomas Reis for VfL Bochum II.