Born in nearby Albany Ciavaglia first became prominent on the local hockey scene with a spectacular career at Nichols High School. He was also very studious, and his high marks saw him proceed to a fine scholastic and hockey collegiate career with Harvard University in 1987. Ciavaglia earned a degree in finance as well as three scoring titles, and player of the year and All American status.
Drafted by the Calgary Flames in the 7th round of 1987, Ciavaglia could never settle on a contract with the Flames. He jumped at the opportunity to return home when the Buffalo Sabres offered him a free agent contract. Ciavaglia knew that even if he was sent to the minors, he would be playing close to home in Rochester with the legendary Amerks.
Ciavaglia lit it up the AHL in his first pro year, scoring 98 points in 77 games. At seasons end he was named the rookie of the year and team MVP for the Rochester Americans. Ciavaglia also earned his first two NHL games as the Sabres called him up for a look that year.
The following year Ciavaglia returned to Rochester and was offensively dominant again. He scored 35 goals and 102 points, and in the playoffs scored 9 goals and 25 points in 17 games en route to leading the Amerks to the Calder Cup championship. Ciavaglia's fine season earned him another 3 game try out with the Sabres, but he failed to impress.
Perhaps somewhat surprisingly, the Sabres released the Amerks scoring star following that season. He split the 1993-94 season playing professionally in Sweden and playing for the United States national team. He was named to the Olympic team for the 1994 Winter Games, and scored 6 points in 8 contests.
Ciavaglia returned to minor pro hockey in North America in 1995-96, signing on with the independent Detroit Vipers of the IHL for their inaugural season. He would stay with the Vipers through the 2000 season when a groin injury forced him out of the game. In that time, Ciavaglia captured every major offensive record in Vipers history. When he retired in 2000, Ciavaglia was the Vipers' all-time leader in games played, goals, assists, points and game-winning goals. He also held the record for most assists in a game and most assists in a season. Ciavaglia also held the Vipers' Playoff records for goals, assists, points and game-winning goals. Ciavaglia won the Bud Polie Award for MVP of the Playoffs, leading the Vipers to the 1996-97 Turner Cup Championship.
After retiring as a player Ciavaglia joined Vipers management. When the team folded in 2001, Ciavaglia put his Harvard degree to work, concentrating on sports financial management.