Is it obligatory for the nephews to maintain ties with their infidel uncle who insults the Divine Being and the Prophet, or is it permissible to cut him off?

The correct view is that there is no obligation to maintain ties of kinship with a disbelieving relative, based on the Prophet's (peace and blessings of Allah be upon him) saying: "Indeed, the family of my father are not my allies; my only ally is Allah and the righteous believers. However, they are relatives with whom I maintain ties through their wetness [i.e., by giving them whatever they need]."

However, if there is a legitimate benefit in maintaining such ties, such as their reversion from disbelief or their giving birth to a Muslim, then it is permissible.

Therefore, you are not obligated to maintain ties with your apostate uncle. However, you must advise him, invite him to Allah, warn him of His punishment, and do not despair of his guidance.