The resolution was moved by Opposition Chief Whip James Sangma, accusing Mondal of having failed to carry out his duties and responsibilities as Speaker.
Mondal admitted the resolution after 13 opposition members comprising of seven United Democratic Party legislators, four Hill State People's Democratic Party legislators and two National People's Party legislators supported it.
UDP legislator Brolding Nongsiej, besides two opposition independent legislators Saleng Sangma and John Leslee K. Sangma, were conspicuous by their absence.
This is the second time the opposition is moving a no-confidence motion against Mondal. Earlier, on March 25, 2015, Mondal survived a no-confidence motion.
Agreeing to face the no-confidence motion, Mondal told journalists: "I am leaving it to wisdom of my colleagues. I will take it positively because it can enrich me so that I can correct myself."
Asked if the no-confidence motion was targeted at the Mukul Sangma-led Congress government, the Speaker said: "I do not know what their motive is."
However, National People's Party legislator James Sangma said he had brought up the resolution against the Speaker as he was curtailing the vibrancy of the legislature.
"He (Mondal) is not allowing the legislature to function properly, which is why we feel it is high time we give a strong message in the form of this resolution seeking his removal," Sangma told journalists.
Meanwhile, Mondal told the House that he had received a letter from Chief Minister Sangma that the resignation of Congress legislator Winnerson D. Sangma from the post of Parliamentary Secretary was accepted.
Later, the Speaker also nominated four members -- Dikkanchi D. Shira, W.D. Sangma, Titosstarwell Chyne and Witting Mawsor -- to the panel of chairmen.
In the 60-member assembly, the ruling Meghalaya United Alliance comprises 30 Congress members, two of the Nationalist Congress Party and 11 independents.