King George III is not mentioned in the Constitution. The Constitution of the United States was written in 1787, more than a decade after the colonies had declared their independence from Great Britain, and four years after independence was formally established by the Treaty of Paris. So King George was not relevant to the Constitution, though its prohibitions against religious tests, noble titles, writs of assistance, and other clauses certainly were a tacit reaction to the actions of the King and Parliament.
It is likely, however, that this question is referring to the Declaration of Independence, which levies many accusations against King George. These accusations ranged from claims that he refused to approve laws that were good for the colonies, to his approval of unjust taxes, to allegations that he urged enslaved people and Native Americans to rise up against the Americans during the early days of the Revolution. Of course, most of these actions, to the extent they actually occurred, were not really undertaken by the King. In fact, it was Parliament that levied taxes, and the king's ministers who formulated imperial policy. For many years, the colonists had actually protested to the King, who they claimed was the protector of their liberties against the corrupt members of Parliament. By levying these accusations against the King, then, they sent a clear message that they were striking out on their own. They were moving from claiming rights as British subjects to rejecting British rule outright.