Mugoša ran as a youth in the place of his birth, Lješkopolje, a rural part of the Donja Gorica suburb in present-day Podgorica.[1] In 1949, Mugoša was the winner of a state junior 1500 meter race for high schoolers in Varaždin.[1] After graduating from high school, he trained in several track clubs over a shorter period of time, including Budućnost, Olimpija Ljubljana, Mladost Zagreb, and AK Partizan.[1] After that, he moved to AK Crvena Zvezda, where he trained until the end of his career.[1] In Belgrade, he was a geography and philosophy student at the University of Belgrade while he recorded Yugoslavia's leading results in the 1500, 3000, and 5000 meters.[5] On 1 July 1956, he ran a personal best time of 13:58.8 in a 5000-meter race in Belgrade,[2] becoming the first person from Yugoslavia to ever run the distance under 14 minutes.[1] At the 1956 Summer Olympics, he progressed to the men's 5000 meter final but dropped out of the race after going out at world record pace.[1]
In the late 1950s, he traveled to the United States where he ran several indoor races. On 1 February 1958, in front of an audience of 12,445 at Boston Garden, Mugoša finished the indoor 2-mile at the Boston AA Games in second place behind Deacon Jones, who won in 9:01.1.[6] On 22 February 1958, he won the men's indoor 3-mile at the AAU Indoor Championships in a time of 13:54.2.[7]
*Distances have varied as follows: 2 Miles (1899–1931), 5000 meters (1933–1939), 3 Miles 1932, (1940–1986) and odd numbered years since 2015, and 3000 meters (1987–2014) and even numbered years since 2014