Graham, R-S.C., who appeared on CBS' "Face the Nation," also predicted that the protests will shift to an armed insurgency within the next 60 or 90 days, and that al-Qaida will come to the aid of the Muslim Brotherhood.
"I would tell the generals that we're going to suspend all aid until you allow a democratic transition. And the aid is just a symbol for the relationship," Graham said. "I would play to the best interests of the military. Stop this before it gets out of hand. We can't support where you're taking Egypt."
He said that the military is not trying to restore order or transition to democracy, as they are jailing the leaders of the former government and attacking peaceful protesters.
Graham argued that General Abdel Fatah al-Sisi needs to take a different direction in his leadership.
"Somebody needs to look al-Sisi in the eye and say, 'You're going to destroy Egypt. You're going to doom your country to a beggar state. You're going to create an insurgency for generations to come. Turn around, General, before it's too late. You're a better man than that,'" Graham said.
Earlier in August, Graham and Sen. John McCain, R-Ariz., flew to Egypt to try to help end the country's political crisis.
Notable deaths of 2014 [PHOTOS]
Marine detained in Mexico is 'highly despondent'