I am replacing a new sink in my kitchen and this piece is from the garbage disposal
Do I just break the glue / putty free and pull it out?
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You need to loosen the 3 screws that push the collar (top piece in your image) against the bracket (bottom piece) into the sink. Once that is done, a lock ring will be visible (underneath where the collar currently sits). Use some pliers to remove that, and then all the pieces on the underside can be removed. You can then break the putty / silicone to remove the gasket from the drain hole in the sink.
All that said, if you're tossing the sink, it's much easier to just buy a new garbage disposal installation kit, which contains all the pieces shown in your image. Install the new kit on your new sink, and then install the old garbage disposal on it.