[1] Born in Smederevo, he studied in Pristina and Vranje, graduating in mathematics at the University of Belgrade Faculty of Philosophy (1932).
He earned a Ph.D. (1933) on a study of differential equations entitled Istraživanja o jednoj važnoj diferencijalnoj jednačini prvog reda (that is, Investigations of an important differential equation of the first order), advised by Mihailo Petrović.
[2] He then worked as a secondary school teacher until 1946, when he visited University of Paris (1946) before joining the faculty at Skopje University in Macedonia where he founded the school of mathematics and two journals, eventually being elected to the Macedonian Academy of Sciences and Arts.
He then worked for the University of Belgrade Faculty of Electrical Engineering (1951–78), where he also became head of the math department (1953) and the founder of the Belgrade School of Functional Equations, Differential Equations and Inequalities, as well the School of Mathematics (1960).
Mitrinović was author or co-author of several well regarded monographs on analytic and geometric inequalities.