A man becomes disillusioned with his wife and divorces her. He lives the rest of his life in a state of celibacy.
Can he still take Holy Communion?
Is he, as presented above, in a state of sin, either mortal or venial?
Going only by what you wrote, imo, he is in the state of mortal sin for breaking his vow and separating from his wife (and children?) without first obtaining the necessary permission from the Church.
Additionally, by him breaking his vow and separating, he will bear some of the guilt for the sins of his wife (and children?), which would otherwise not have been committed if he were where he vowed before God to remain until death.
He will also pay for the neglect of the duties he was bound to carry out as a husband and as a father. Before God he will answer for this neglect toward his children as well as his spouse.
Can he receive Holy Communion? - No. Regardless of the reason he divorced his wife - even if he was in imminent danger of being murdered by her, he is not permitted to receive communion without permission from the Church - or in today's world, not without permission from at least one of the trad priests - or perhaps not without permission from one of the trad bishops.
That's how it goes. Holy Mother considers (used to consider) it a very serious offense to separate from bed, much more so from bed and board - civil divorce / celibate life was rarely permitted and even then, she only allowed it only after the Church, not the wife or husband, was satisfied that every possible effort was exhausted to remedy the situation.
In this day and age though, where there is no Church authority reliable enough to grant or deny any permission, best to get with a trad priest first and go from there before receiving communion.