Performing cardiac surgery under cardiopulmonary bypass (CPB) and circulatory arrest (CA) provokes the development of complications caused by tissue metabolism, microcirculatory disorders, and endogenous nitric oxide (NO) deficiency. This study aimed to investigate the potential mechanisms for systemic organoprotective effects of exogenous NO during CPB and CA based on the assessment of dynamic changes in glycocalyx degradation markers, deformation properties of erythrocytes, and tissue metabolism in the experiment. A single-center prospective randomized controlled study was conducted on sheep, n = 24, comprising four groups of six in each. In two groups, NO was delivered at a dose of 80 ppm during CPB (“CPB + NO” group) or CPB and CA (“CPB + CA + NO”). In the “CPB” and “CPB + CA” groups, NO supply was not carried out. NO therapy prevented the deterioration of erythrocyte deformability. It was associated with improved tissue metabolism, lower lactate levels, and higher ATP levels in myocardial and lung tissues. The degree of glycocalyx degradation and endothelial dysfunction, assessed by the concentration of heparan sulfate proteoglycan and asymmetric dimethylarginine, did not change when exogenous NO was supplied. Intraoperative delivery of NO provides systemic organoprotection, which results in reducing the damaging effects of CPB on erythrocyte deformability and maintaining normal functioning of tissue metabolism.