Bradford were handed a six-point deduction after entering administration in February and have struggled to overcome that sanction.
Local businessman Marc Green completed a takeover in March, but the club have won just four league fixtures in 2014 and Sunday's 46-18 defeat to Salford Red Devils represented the latest blow to their hopes of staying in the top flight.
Cummins and assistant coach Lee St Hilaire were relieved of their positions on Monday.
A spokesperson for the club’s board of directors said "This is a decision which has not been made lightly and Bradford Bulls would like to thank both Francis and Lee for their efforts over the years.
"Both have worked under difficult circumstances during their time here, but the club recognises that a change of direction is required.
"The board of directors has the upmost respect for both Francis and Lee and wish them well with their futures."
Bradford will now begin the process of identifying and hiring a new head coach in an attempt to turn their fortunes around.
Club skipper Matt Diskin has agreed to act as temporary player-coach ahead of Friday's visit of Hull Kingston Rovers.