Dobkin studied in New York at the City College of New York, Columbia Unversity, the Art Students League, and the Leonardo da Vinci Art School. In his paintings Dobkin brought an expressionistic style and dark rich palette to figurative subjects; he also worked in graphic media.
Dobkin taught and lectured widely, and for many years was director of the art school of New York's Educational Alliance. He authored Principles of Figure Drawing, 1948, which was issued in its third, revised edition in the year of his death; Alexander Dobkin's Travel Sketchbook, 1966; and was the illustrator of a number of classsical works of literature.