Why does angina cause pain and breathlessness?

Lack oxyen. Lack of oxygen causes pain in any muscle when oxygen demand out strips suply . In the legs its called cludication. As for the shortness of breath it can be due to the dysfunction of the left ventricle due to poor oxygen suply. Much like an engine sputters if the fuel line is clogged. Along with heart failure pain and anxiety can also cause shortness of breath.
Injury. The pain is a common symptom to injury -- in this case hypoxic/anoxic injury and the breathlessness is due to reduced perfusion (functional circulation) to the lung -.