Mendez made his official debut at the 1996 Summer Olympics in Atlanta, where he competed in the men's 60-kg class. He was defeated by an ippon and a kata guruma (shoulder wheel) from Mongolian judoka and eventual bronze medalist Dorjpalamyn Narmandakh in his opening match. Mendez gave himself a chance for an Olympic bronze medal through the repechage, but crashed out immediately in another ippon defeat to Great Britain's Nigel Donohue with only 20 seconds remaining.[4][5]
Eight years after his official Olympic debut, Mendez qualified for his third Puerto Rican squad, as a 30-year-old, in the men's half-lightweight class (66 kg) at the 2004 Summer Olympics in Athens. Earlier in the process, he finished third and received a berth on the Puerto Rican Olympic team from the Pan American Championships in Margarita Island, Venezuela.[8][9] Unlike his two previous Olympic stints, Mendez got off to a difficult start with an unprecedented deadlock and a golden score in his opening match against Spain's Óscar Peñas, forcing them to fight in the second round. After nine seconds, Mendez came his third chance of an Olympic medal to a dramatic halt by a single leg takedown (kuchiki taoshi) from Penas.[10][11][12]