Muttis (sometimes recorded as Mutis) started his career with Argentine club Wanderers. In 1920, he joined Club Atlético Atlanta where he was part of the team that won the Copa de Honor in 1920.
Muttis joined Boca Juniors in 1923, the same year that he made his international debut. He won a total of 9 championships with the club. Muttis made a total of 237 appearances for Boca Juniors, spanning ten seasons earning the nickname "Ramón el Fuerte (Ramón the Strong)".
Muttis played in two editions of the Copa América, winning the tournament in 1925 and finishing second in 1926. He was part of the Argentina squad for the 1930 FIFA World Cup but he only played in one game, against France.
Muttis retired in 1932 but came out of retirement in 1936 to play for Argentinos Juniors. He went on to become player-manager of Almagro leading them to the 2nd Division championship in 1937[1] and in 1940 he was the manager of the Argentinos Juniors squad that won the 2nd division championship.[2]