A method for providing at least partial bypass of the heart to supplement the pumping function of the heart to thereby enable the surgeon to perform various surgical procedures thereon includes providing a circulatory assist system having a portable extracorporeal axial flow pump with a pump housing, a rotating pumping member disposed in the pump housing and inlet and outlet cannulated tubes respectively connected to inlet and outlet ports of the pump housing, accessing the patient's left atrium of the heart with the inlet cannulated tube, accessing the aorta with the outlet cannulated tube, actuating the rotating pumping member to draw oxygenated blood from the left atrium of the heart through the lumen of the inlet cannulated tube and into the inlet port of the pump housing whereby the pumping member imparts mechanical energy to the oxygenated blood passing through the pump housing and directs the oxygenated blood through the outlet port and through the lumen of the outlet cannulated tube to be transferred by the aorta to the systemic arteries and permitting the right side of the heart to function whereby oxygen-depleted blood returning through the systemic veins to the right atrium is directed through the right ventricle to the patient's lungs for oxygenation and subsequent pulmonary circulation.