Just to clarify here, we are talking about a purely acoustic flat-top guitar with a one-piece saddle set into the bridge plate, with no electric pickups of any kind?

Usually the saddle is simply a snug fit in a slot routed into the bridge plate. It may have been glued in, but that should not have been necessary.

I'm reluctant to recommend brute force. If you have access to a good tech or a luthier, ask them about it.