If this was installed correctly, it will stick really hard to the cement board. You're going going down to the studs, and removing the backer board and everything, to start over. If it wasn’t installed correctly, trying to save backer board with blobs of mortar on it is not something to do. Go down to the studs.

Gutting this is filthy dusty work. Take care of the PPE. Gloves. Long sleeves. Heavy shoes. Ear plugs. Goggles. You need a respirator. Not a dust mask. You also need to tape off the bath double with plastic and zip poles. A garden sprayer with water can help with keeping the dust down. Open a window, and put a fan in it. You will still need to do a massive wipe down cleanup.

Reciprocating saw. Pry bars. Contractor trash bags, or 5 gallon bucket to the dumpster. Start cutting with a saw from the top down, until you can get a purchase with a pry bar. There can be electrical runs in the cavity. Get a work light on an extension cord and turn off the breaker until you are done. Most municipalities do not allow you to dispose of construction debris with household trash. Find out where and how the debris goes.

Thanks for the detailed reply!