One of the best games in Mira's collegiate career came in the 1962 Gotham Bowl against the Nebraska Cornhuskers. Despite playing in twenty-degree weather in front of less than a thousand fans at Yankee Stadium, Mira threw for 321 yards, a Miami school record at the time, and was named the bowl game's most valuable player. Despite Mira's efforts, the Cornhuskers won, 36-34.
Mira later played 19 games with the Montreal Alouettes of the Canadian Football League in 1972 and 1973, completing 92 of 168 passes for 1356 yards and 11 touchdowns and eight interceptions in 1973. With the Birmingham Americans of the WFL in 1974 he was MVP of their championship game victory, completing 155 of 313 passes for 2248 yards and 17 touchdowns and 14 interceptions during the season. In 1975, with the Jacksonville Express of the World Football League, he completed 123 of 254 passes for 1675 yards and 12 touchdowns and interceptions. He finished his career in 1977, playing six games for the Toronto Argonauts.