He was a goalkeeper and played for Forfar Athletic and made 104 appearances. He was then signed for Dundee United by Jerry Kerr, for whom he made 170 appearances. This is still the second most appearances made by a goalkeeper for Dundee Utd, behind keeping legend Hamish McAlpine. He was then given a free transfer by Jim McLean, after ten years of loyal service to the Utd cause, where he finished his 16-year professional playing career with Southend United after only 13 appearances.
After a spell coaching the Bristol City youth team between 1974 to 1978, where he was part of the backroom staff that won promotion to the then English First Division, he began his management career in Denmark with Nørresundby managing the local side Norresundby, gaining promotion in his first season there. He returned to Scotland in 1980 when he was appointed manager of Dundee, winning promotion to the Scottish Premier League with the club, again in his first season in charge. After several high profile departures from the Dundee first team, Mackay eventually left the club in 1983.
After a short time away from the game, Bobby Gould approached him to be his assistant at Coventry City. Bobby was sacked after a poor run of results and Don was asked to take charge, where the club staved off relegation by famously winning their last three games of the season, to retain their First Division Status.
Following the sack at Coventry, Mackay went to work as reserve-team coach at Rangers, alongside ex playing colleague Walter Smith and the manager Graeme Souness. Despite a successful spell at Rangers, Mackay wanted to manage in his own right, and therefore moved onto Blackburn Rovers. They narrowly missed the play-offs in his first season in charge, but did win the Full Members Cup, beating the likes of Chelsea, Everton and Charlton along the way.
In the next two seasons at Blackburn they made the play offs, losing out on promotion both times. Following a relatively poor final season in charge, he was relieved of his position there and went onto manage Fulham, His first season at Fulham was promising but results deteriorated the following year and following a defeat at Leyton Orient he was dismissed, results did not improve and Fulham were eventually relegated to the Fourth Division.