How does the respiratory system affect the cardiovascular system?

No O2 no function: Easy think of it as an engine the blood is the gas that supplies the body and you need to have oxygen to run the body, so when you breathe te blood gets oxygenated and delivered by the cardiovascular system to the rest of the body.

Directly: If you don't cary out gas exchange (o2--co2)in the lungs, then your blood ph will fall (acidosis), and the heart will experience arrhythmias, ultimately asystole and death.