Trump, the presumptive Republican nominee, has asked a state court to overturn Bellows' decision.
Trump's lawyers argued in a court filing about the Maine decision that Bellows, a Democrat, is a "biased decision-maker" who lacks the legal authority to remove Trump from the ballot.
The application accuses Bellows of making "numerous errors of law" and acting in an "arbitrary and capricious manner".
The number of states in the US that have banned Trump from voting has increased to two. Bellows said he had a "sacred obligation" to uphold the law on the Trump decision.
Trump was removed from the ballots in Maine and Colorado after allegations that he "incited the 2021 US Capitol riot".
The US Constitution prohibits people "engaged in insurrection or rebellion" from holding federal office.