Although born in Pittsburgh, Cassidy was raised in Philippi, West Virginia, 120 miles south of Pittsburgh. He played basketball (center position) and football (tackle) for Philippi High School. At that time, he was an imposing figure in both venues, being the tallest player in the conference. Early in his academic career, Cassidy attended West Virginia Wesleyan College, in nearby Buckhannon, WV, where he was a member of Alpha Sigma Phi Fraternity. He later attended Stetson University in DeLand, Florida, as a Speech major. Active in student government, he also played basketball for the Hatters, averaging 17 points and 10 rebounds in his only season as a player.

Upon graduation with a degree in speech and drama, he married Margaret Helen in 1956, and they moved to Dallas, Texas. His acting business took off when he worked as a mid-day disc jockey on WFAA-AM in Dallas, Texas. He also occasionally appeared on WFAA-TV Channel 8, playing "Creech," an outer space creature on the "Dialing for Dollars" segments on Ed Hogan's afternoon movies. An accomplished musician, Cassidy moonlighted at Luby's Cafeteria in the Lochwood Shopping Center in Dallas, playing the organ to entertain patrons. In 1957, Margaret gave birth to their son, Sean, and in 1960 daughter Cameron was born.

On November 22, 1963, shortly after the John F. Kennedy assassination, Cassidy interviewed several of the witnesses, including two very close witnesses, William and Gayle Newman, after the Newmans had appeared on WFAA-TV, but before they left to go to the Dallas Sheriff’s office (no tape exists of that interview as the radio station did not start recording its broadcasts until about 1:45 PM). He also interviewed the manager of WFAA-AM who was in the Book Depository and saw a man run out of the building shortly after the shooting. The manager offered several times to talk to Dallas police who repeatedly refused to interview him.

Cassidy's unusual height (6 feet 9 inches tall, or 206 cm) gave him an advantage in auditioning for unusual character roles. He is probably best known for playing the tall butler, Lurch (in which role he feigned playing the harpsichord), and the "helpful hand in a box" character named Thing, on the 1960s American television series The Addams Family. (A crew member would take over the "Thing" role in those scenes which had both characters.) It was Cassidy who came up with the "You rang" line, which was so funny that it was incorporated in the show, where the Lurch character had originally been intended to be nonspeaking.

Cassidy had a regular role on NBC's The New Adventures of Huckleberry Finn as the blood-foe of Tom Sawyer and Huck, Injun Joe.

Cassidy portrayed the voice of the more aggressive version of Balok in the Star Trek episode "The Corbomite Maneuver", and he played the role of the android Ruk in the episode "What Are Little Girls Made Of?." He also voiced the Gorn in the Star Trek episode "Arena".

Cassidy did more work with Star Trek creator Gene Roddenberry in the early 1970s, playing Isiah in the pilots of the post-apocalyptic dramas Genesis II and Planet Earth.

Ted appeared in several episodes of I Dream of Jeannie in 1968. Once appearing as the master to Jeannie's devious sister in part 3 of the 4-part episode "Genie, Genie, Who's Got the Genie?", and again in the episode "Please Don't Feed the Astronauts" in which he plays Jeannie's cousin.

In the two part episode entitled "The Return Of Bigfoot", Cassidy appeared as "Bigfoot" (played by André the Giant in a previous two parter). He even provided the vocal effects for Bigfoot. He reprised the role in the episode Bigfoot V.

In the episode "The Dahlia Feud" 12 April 1967 (Season 5, Episode 30) he played Mr. Ted, a large, muscular gardener who was planting Dahlias for Mrs. Drysdale.