Dragan performed in more than sixty theatrical plays, movies and television productions, between 1971 and 1999. On 17 November, 2000, Maksimović was brutally attacked in Zeleni Venac, in day-time, by a group of FK Rad supporters (after their team lost a match against Obilić), who assumed he was Romani. He died on 4 February 2001 in the hospital.
On the initiative by film director Goran Marković, a commemorative plaque was placed at Zeleni Venac on 18 November 2006.
The perpetrators remain at large.