Kavanagh, who turned out for Carlisle at the end of his playing career, was appointed as the permanent successor to Greg Abbott last September after a successful stint in caretaker charge.
However, the Brunton Park outfit were subsequently relegated from League One and have made a poor start to life in England's fourth tier, collecting just two points from five games.
A 5-0 defeat at Cambridge United on Saturday represented the final straw for Carlisle's board, who have placed club captain Paul Thirlwell and goalkeeping coach Tony Caig in temporary control of first-team affairs.
A statement from Carlisle on Monday read: "Regretfully, it has been decided to dispense with Graham's services after a very difficult and disappointing start to the season.
"Over the course of approximately one year Graham has managed significant change within the club, including the youth management and successful achievement of Category 3 in the EPPP process, the introduction of 'strength and fitness coaching' and diet control, and major change of the first team squad over the summer period.
"Unfortunately results on the field have not reflected that effort and hard work and from the 40 league games last season, following Greg Abbott’s departure, and through the five league games this season there has been an average of one point per game.
"This resulted in relegation to League Two in May 2014 and it was felt we were continuing to head in the same direction this season. Saturday's result at Cambridge was a 'tipping point' for those concerned with the running and management of Carlisle United Football Club."
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