Mirsky was born in Russia on 19 December 1918 to a medical family, but his parents sent him to live with his aunt and uncle, a wool merchant in Germany, when he was eight.

Because of the evacuation of London during the Blitz, students at King's College were moved to Bristol University, where Mirsky earned a master's degree.

In 1953 Mirsky married Aileen Guilding who was, at that time, a lecturer in Biblical History and Literature at Sheffield but later became a professor and Head of Department.

In modern polyhedral combinatorics, this result can be seen as a special case of Carathéodory's theorem applied to the Birkhoff polytope.

[2] In the mid 1960s, Mirsky's research focus shifted again, to combinatorics, after using Hall's marriage theorem in connection with his work on doubly stochastic matrices.

In this area, he wrote the textbook Transversal Theory (Academic Press, 1971), at the same time editing a festschrift for Richard Rado.

[3] He derived conditions for pairs of set families to have simultaneous transversals, closely related to later work on network flow problems.

[2] Mirsky's theorem, a dual version of Dilworth's theorem published by Mirsky in 1971, states that in any finite partially ordered set the size of the longest chain equals the smallest number of antichains into which the set may be partitioned.