Born in Oakland, California, Vukasin received an Bachelor of Arts from the University of California, Berkeley in 1950 and a Juris Doctor from the University of California, Berkeley, Boalt Hall School of Law in 1956. He was in the United States Army from 1951 to 1953. He was a trial attorney of the Division of Highways, Department of Public Works, State of California from 1956 to 1957.
He was in private practice in San Francisco, California in 1958, and in Oakland, California from 1959 to 1968.
He was a Commissioner of the California Public Utilities Commission from 1969 to 1974. He was a judge on the California Superior Court from 1974 to 1983.
On September 13, 1983, Vukasin was nominated by President Ronald Reagan to a seat on the United States District Court for the Northern District of California vacated by Stanley A. Weigel. Vukasin was confirmed by the United States Senate on September 20, 1983, and received his commission the same day.
He served until his death, in 1993.