The 57-year-old, who was in his second spell as the Mariners' boss, had been in charge since April 2017.
Saturday's 3-0 loss at Crawley Town, however, stretched Grimsby's winless run to 12 games, prompting the board to take action.
"The board would like to place on record their disappointment with this outcome, but believe there is little choice but to move forward with a new management team," a club statement read.
"As highlighted in recent weeks, this is not a decision we have taken lightly.
"While the board continued to back Russell throughout the season and the recent transfer window, yesterday's 3-0 defeat and a winless run of 12 games cannot be ignored.
"Despite speculation to the contrary, Russell was on a six-month rolling contract, allowing the club the flexibility to make this decision.
"He had a strong working relationship with the board and all involved are disappointed to see a good, hardworking and honest man, who cared intensely about the club, lose his job."
Slade leaves Grimsby with the club 17th in League Two, nine points above the relegation zone, and without a victory since December 9.