The native of San Luis, Pinar del Río, was a right-handed pitcher whose nine-year career included seven games pitched in Major League Baseball for the 1961 Minnesota Twins.

Cueto was signed in 1956 by legendary scout Joe Cambria of the Washington Senators of 1901–1960, and was in his sixth year with the organization when he was recalled from Triple-A Syracuse during the MLB franchise's first season as the Twins.

He was a starting pitcher in five of his seven Minnesota appearances, including his MLB debut on June 18, 1961, against the Chicago White Sox at Comiskey Park.

But, one out away from his first big-league victory, Cueto surrendered a game-tying home run to pinch hitter Billy Goodman and was removed from the contest.

Relief pitcher Pedro Ramos then gave up a game-winning homer to eventual Baseball Hall of Famer Nellie Fox.