Punch out the motor out of the spindle. I ended up using a 1 3/8" socket on the bottom so the motor will just fall out easier. Put all of this on top of an anvil. Place the punch in the center hole and then popped it with a hammer 2 or 3 times. The motor will fall right out.
There will be a bearing on the inside of the spindle and it will start to loose some of the metal clips from the inside of it now that the core is removed. Needle nose pliers are needed to pull them out from the inside of the spindle so you don't mark up the outside face. If these clips aren't pulled out it will be very hard to push the quartz clock movement in the hole when it's time to assemble the whole thing.