Mulvey broke into the major leagues with the Providence Grays of the National League in 1883. He played in a total of four games for the Grays, but his tenure there was not without some excitement. In June 1883, Grays outfielder Cliff Carroll had antagonized one of the team's fans – a man named Jimmy Murphy – by spraying Murphy with a water hose as the fan was watching the Grays warm up. Enraged, Murphy went home and retrieved a gun. Mulvey was not seriously injured in the shooting, and Murphy was arrested. He returned to the park, waited until the players were leaving the field at the end of the game, and fired a shot at Carroll. His aim was off, and the bullet struck Mulvey in the shoulder. Mulvey sustained only a flesh wound, and Murphy was arrested. Mulvey was traded to the Philadelphia Quakers shortly after the shooting, and he played in another three games that season after switching to third base. The following year, Mulvey began playing regularly for the Quakers, appearing in 100 of their 120 games. He would play regularly for Quakers/Phillies through the 1889 season.
Later career
In 1890, following many other stars of the National League, he jumped to the Players' League, where he joined the Philadelphia Athletics as their starting 3rd baseman. When the Players' League folded after a single season, the Athletics moved to the American Association, and Mulvey went with the team. The 1892 season saw Mulvey rejoining the Phillies, where he was now the back-up to Charlie Reilly. The following season saw him traded to the Washington Senators, where he split 3rd base duties with 3 other players: Duke Farrell, Cub Stricker, and Sam Wise. Mulvey did not play in the 1894 season, but he returned to baseball for the 1895 season, playing with the Brooklyn Grooms, as the backup to Billy Shindle. For his career, Mulvey batted.261, with 28 home runs. According to his statistics, his best year was 1890 with the Philadelphia Athletics, in which he achieved career highs for RBIs, walks, on-base percentage, slugging percentage and doubles. He almost equaled his career bests for home runs and batting average that year as well. The most home runs he had in any one year was 6, with the Phillies in 1884 and 1889, and his best batting average was.289, also with the Phillies in 1889. Along with five other players, Mulvey still holds the record for most errors by a third baseman in a single game, 6, set on July 30, 1884.
