The US-based organization has also terminated the contract of its title sponsor, Russian chemicals company Uralkali.
Uralkali is owned by Mazepin's billionaire father Dmitry, a close aide of Russian President Vladimir Putin, through his company Uralchem.
Haas said news of Mazepin's replacement is expected early next week.
Among the drivers being considered are the team's reserve Pietro Fittipaldi, who stood in for Romain Grosjean for two races in late 2020 after the Frenchman's horrific crash in Bahrain, Indian Formula 2 driver Jehan Daruvala and Alpine reserve driver Oscar Piastri, the current F2 champion.
Haas said in its statement: "As with the rest of the Formula 1 community, the team is shocked and saddened by the invasion of Ukraine and wishes a speedy and peaceful end to the conflict."
Mazepin's departure from F1 had been expected since Russia launched an invasion of Ukraine on 24 February. Dmitry Mazepin was one of several prominent Russian businessmen invited to a meeting with Putin in the Kremlin a few hours after the invasion began.
Haas repainted their cars on 24 February in the middle of the first Formula 1 pre-season test in Spain, to remove the red, white and blue colors that were on the car to represent the Russian flag as Mazepin. Joined in early 2021. ,
Motorsport's governing body FIA has blocked Russian drivers from being banned from international competition. It says they must compete as neutral athletes, and sign a document agreeing not to support the invasion.
Motorsport UK was one of several national motorsport authorities this week banning Russian competitors from participating in events in the UK.
There is debate as to whether this would ban a Russian driver from the British Grand Prix, as an F1 driver's super-license contains a clause that requires national authorities to allow him to race.
But the issue is now controversial after Haas decided to end his relationship with Mazepin.