Illuzzi is the son of Vincent Illuzzzi, Sr. (1920-2013), born in Giovinazzo, Italy, who emigrated to the US at the age of 17 and became a granite sculptor. Illuzzi, Sr. carved one of the largest monuments ever shipped from Barre, a granite sculpture depicting a person chained to a wall that is part of the Taras Shevchenko Memorial located near Dupont Circle, Washington DC. He also supported the restoration of the Old Labor Hall and the Vermont Granite Museum in Barre.