The most likely "diepe kloof" (deep canyon) you're referring to in Arizona is the Grand Canyon.
The Grand Canyon is a steep-sided canyon carved by the Colorado River over millions of years. It's one of the Seven Natural Wonders of the World and is famous for its layered rock formations that reveal billions of years of geological history.
The Grand Canyon is enormous. It's 446 kilometers (277 miles) long, up to 29 kilometers (18 miles) wide and attains a depth of over 1.8 kilometers (1.1 miles). The canyon and adjacent rim are contained within Grand Canyon National Park, the Kaibab National Forest, the Grand Canyon National Game Preserve, and the Navajo Nation Reservation.