A 10th-round selection (129th overall) in the 1978 OHL Midget Draft, Cunneyworth suited up for his first year of junior hockey with the Dixie Beehives of the former OPJHL (now OJHL).

Following the season, Cunneyworth was chosen in the eighth round, 167th overall, by general manager Scotty Bowman of the Buffalo Sabres in the 1980 NHL Entry Draft.

He played primarily on the CPR (Canadian Pacific Railroad) line with young teammates Steve Patrick and Lindy Ruff.

Cunneyworth spent the playoffs with Rochester, scoring four goals in nine games, as the Americans lost to the Binghamton Whalers in the South Division finals.

In 16 playoff games, Cunneyworth had four goals and eight points, helping the Americans win the 1983 Calder Cup Championship defeating the Maine Mariners.

In 17 post-season games, Cunneyworth scored five goals and 10 points, as Rochester lost to the Maine Mariners in the 1984 Calder Cup finals.

Cunneyworth was granted permission by Sabres GM Scotty Bowman to attend the Pittsburgh Penguins training camp/preseason roster.

Though he was considered, Cunneyworth was not selected by Wales Conference Coach Mike Keenan for the NHL All-Star Game, though his point totals ranked among the league leaders for his position at midseason.

Cunneyworth recorded a career game-high 27 minutes in penalties in a game played February 11, 1989 at Quebec, where he was involved in two on-ice fights versus Marc Fortier and Darrin Kimble during a line brawl.

On June 17, 1989, the Penguins traded Cunneyworth, Rick Tabaracci, and Dave McLlwain to the Winnipeg Jets for Jim Kyte, Andrew McBain, and Randy Gilhen.

Cunneyworth suffered through an injury-plagued 1990–91 season (broken leg/ankle injuries) after being hit by an Ulf Samuelsson shot during Hartford's December 21, 1990 game at Montreal.

In seven playoff games, Cunneyworth had three goals (tied for team lead) as Hartford lost to the Montreal Canadiens in the first round of the postseason.

Cunneyworth played in six playoff games with Chicago, getting no points, as the Blackhawks lost to the Toronto Maple Leafs in the first round of the postseason.

He scored 12 goals and 36 points, as he helped the club qualify for the playoffs for the first time in team history, as Ottawa finished in seventh place in the Eastern Conference.

After four seasons with the Senators, Cunneyworth was given his release by newly hired GM Rick Dudley and became a free agent, and on August 27, 1998, he signed with the Buffalo Sabres.

On September 8, 2000, Cunneyworth officially announced his retirement from playing hockey and was named the new head coach of the Rochester Americans by Sabres GM Darcy Regier.

After the 1999–2000 season, Cunneyworth retired from being an active player and was named the head coach of the club by Sabres GM Darcy Regier.

Cunneyworth was fined by the league for throwing a water bottle at referee Chris Rooney due to a disputed goal call vs Syracuse.

In the playoffs, the Americans defeated the Syracuse Crunch and Hamilton Bulldogs before losing to the Milwaukee Admirals in the Western Conference finals.

The team struggled, finishing under .500 for the first time since Cunneyworth became the head coach, as Rochester went 37–39–2–2 for 78 points, fifth in the North Division, missing the playoffs.

On April 14, 2010, Atlanta's newly hired general manager Rick Dudley fired Anderson and all of his assistant coaches, including Randy Cunneyworth.

On July 20, 2010, Pierre Gauthier, the GM of the Montreal Canadiens hired Cunneyworth to be the head coach of their AHL affiliate, the Hamilton Bulldogs.

In the post-season, he led the club to series victories over the Oklahoma City Barons and Manitoba Moose before losing to the Houston Aeros in the Western Conference finals.

[3][4] In contrast to Quebec nationalists, most regular fans were not bothered by this issue, as "a common refrain heard in Montreal is that fans would be willing to support the hiring of a coach who can't speak French if it were someone like the accomplished Mike Babcock, or local hero Kirk Muller" (indeed, no such controversy occurred when Muller was interim head coach on August 13, 2020).

[5] The Canadiens were also criticized for failing to defend their interim head coach against the attacks from Quebec nationalists and politicians, as it "is not Cunneyworth’s fault that he speaks only English.

That game saw forward Tomáš Plekanec score a rare 3-on-5 shorthanded goal; a feat which had not been accomplished in 25 years by a fellow Hab.

In a staff reorganization, Cunneyworth returned to his previous position in the Sabres' player development program after Dan Lambert was hired as head coach of the Americans on May 16, 2016.

On January 8, 2014, Cunneyworth was promoted to special assistant and player development coach/administrator of the AHL's Rochester Americans by the newly-hired Sabres president of hockey operations Pat Lafontaine.

In the summer of 2015, Cunneyworth was considered as a candidate for the vacant head coaching positions with both the Sabres, which went to Dan Bylsma, and the Rochester Americans.

As a player, Cunneyworth was known to be very physical, quick, and possessed the ability to provide reliable secondary scoring as well as handle defensive assignments.