He was born in Boston, Massachusetts. His family moved to Cleveland, Ohio, when McVey was still in high school. Following his graduation he attended the Cleveland School of Art. He left to attend Rice University, where he played football under Coach John Heisman in 1924 while studying illustration. He returned to art school in Cleveland but did not study sculpture there because "his personality (was) incompatible with that of Herman Matzen, who headed the department." While studying at night he worked for the Gandola Brothers making tombstones. In 1929, a patron financed a "shoe-string' budgeted trip to Paris, where he studied with Despiau and Gimond as well as earning a meager living as one of three American guides at the Louvre Museum.

In 1932, after three years in Paris, he returned to Cleveland and taught at the Cleveland Museum of Art. Shortly afterwards he was employed by the Works Progress Administration for whom he created several works using the direct carving approach.

Around 1935, McVey returned to Texas to teach at the University of Texas in Austin. During World War II he entered the army and was stationed at Fort Randolph Army Base, where he taught plane and ship silhouette "recognition." Called up to explain why his students were being taught art in their classes, a test of his students showed that they scored higher in "recognition' tests than students taught in the traditional manner, and his approach was subsequently adopted by the other classes.

Following his discharge from the army McVey, then married to "radical" ceramicist Leza McVey, moved to Cranbrook Academy of Art in Bloomfield Hills, Michigan, where he taught sculpture (1947–1954) and she studied with Maija Grotell.

He died in Cleveland, Ohio on May 30, 1995