Díaz was born in La Rioja. He won the World Youth Cup in 1979 with the Argentina under-20 team alongside Diego Maradona. He also played in the 1982 FIFA World Cup and scored against Brazil in Argentina's 3–1 defeat. It had been rumoured that he and Maradona were involved in a feud which prevented Diaz from playing for Argentina in the 1986 and 1990 World Cups. However, this was denied by Maradona in his autobiography "El Diego", claiming that he had told the then-Argentina manager, Carlos Bilardo, that he wanted Diaz in both the 1986 and 1990 World Cup squads.
Diaz played in River Plate's youth system under Norberto "El Pacha" Yacono, who recommended Diaz to his "Maquina" Teammate Angel Labruna who was coaching the senior side.
Díaz played as a forward. His opening game in the Argentine First Division was on 13 August 1978, a game where River Plate beat Colón de Santa Fe by 1–0. He scored his first goal on 30 August of that year, playing against Quilmes Atlético Club. His last game was on 13 March 1993.
Díaz served as the manager of River Plate between 1995 and 2003, in that time he guided the club to victory in the 1996 Copa Libertadores as well as collecting five league titles and the Supercopa Sudamericana.
Ramón Díaz served as manager of League Two English club Oxford United between 2004 and 2005, despite already having achieved considerable success in his native Argentina. At the time, Diaz told the media: "I like English football and I wanted to get first-hand experience of it...I'd seen plenty of it on television...It's also very interesting to work at this level, because it's completely different from football at the top." It was also claimed that neither Diaz nor any of his five backroom staff were being paid by Oxford United for their services.
In 2007 he was appointed head coach of San Lorenzo, in the Argentine Primera. In his first season with the club he led them to the Clausura 2007 championship title, the club's first title in six years. In 2008, Diaz was confirmed as the new Club América coach. Although the club did not reveal specific details about Diaz' contract, he was reportedly offered 1.5 million dollars per year including performance-related bonuses which could have taken his total earnings to 6 million dollars. He was fired on 10 February 2009.
On 5 March 2012, Ramón Díaz quit Independiente, The 52-year-old coach resigned from his position at the King of Cups, who had been struggling and found themselves at the very bottom of the table.
Later that year he was appointed coach of River Plate for the third time.