Ive got a Honda XR 125 L motorcycle and it is very quiet, I have taken off half the exhaust which makes the bike much louder. I wanted to know if this causes any damage to the actual engine. Does it cause over heating as well? Ive disconnected the end part of the exhaust from the other half which runs directly into the engine.

It will cause it to lose power because that exhaust was finely tuned to get the most out of that very small engine.

Loud does not equal fast.