Joseph Finley was born on June 29, 1987 in Edina, Minnesota. Finley attended University of North Dakota and was selected in the first round of the 2005 NHL Entry Draft by the Washington Capitals.
A serious injury suffered in 2009 slowed Finley's progress and limited his game action. He would split time between the Capitals' AHL and ECHL affiliates for two seasons, though never suit up for Washington.
Finley would join the Buffalo Sabres organization for the 2011-12 season, serving as a defensive, rugged defenseman for the Sabres' affiliate, the Rochester Americans. He would also appear in five games for the Sabres during the 2011-12 season, recording 12 minutes in penalties along the way.
On January 14, 2013, Finley was waived by the Buffalo Sabres and subsequently claimed by the New York Islanders. He would see action in 16 games for New York during the lockout shortened season, recording his first NHL point along the way.