Grady was born in Chattanooga, Tennessee, and arrived in California in 1924. While visiting a high school pal in Los Angeles in 1924, roly-poly Grady Sutton made the acquaintance of his friend's brother, director William A. Seiter, who used him as an extra in The Mad Whirl (1925). Grady enjoyed himself in his bit role, and decided to remain in Hollywood, where he spent the next 47 years playing countless minor roles as dimwitted Southerners and country bumpkins. He specialized in playing slightly befuddled Southerner who added comedic bits to comedies and dramas.

Usually appearing in comedies, Grady supported such master clowns as Laurel and Hardy. His most famous association came from appearing in four movies with W.C. Fields (who reportedly refused to star in 1940's The Bank Dick unless Grady was given a good part), in The Pharmacist (1933), The Man on the Flying Trapeze (1935), You Can't Cheat an Honest Man (1939) and The Bank Dick (1940).

He can also be seen in such screen classics as My Man Godfrey (1936), Stage Door (1937), Alexander's Ragtime Band (1938), Angels Wash Their Faces (1939), Anchors Aweigh (1945), White Christmas (1954), A Star Is Born (1954) (1954) and 0058385 (1964).

He was also a regular on "The Egg and I" (1951) and "The Pruitts of Southampton" (1966-1967) TV series. In total, he appeared in over two hundred feature films and short subjects spanning 1924 to 1979. His final film appearance was in Rock 'n' Roll High School (1979). Grady went into virtual seclusion after the death of his close friend, director George Cukor. In 1994 Grady moved to the Motion Picture and Television Home and Hospital in Woodland Hills, California, where he died of natural causes.