How do I seperate the part in the middle in a clock mechanism?
The brass part may be ultrasonically welded into the plastic piece. The part is pressed into place under pressure with it being vibrated at the ultrasonic frequency. This causes the plastic to soften and flows around the brass part locking it into place. The brass piece often is made with groves or knurling on the sides which give the plastic something to flow around and keep the part in place. 

In this case the hex shape on one side is part of the grip system that ensures that the brass part does not turn. 

If you have ever used plastic project boxes they often have brass inserts that accept the screws that hold the lid on. These inserts are installed just like I describe above.

This all drives to the conclusion that if you try to remove the brass insert you will almost certainly destroy the black plastic piece. If not destroyed you would have to find some messy way to try to glue the brass piece back in place - - - if the glue/epoxy used even will bond with the plastic.