Really would be best to post that picture for better reply's.
No it's not chiseled out it's cut out.
Enough needs to be removed so the new piece will be sitting on a floor joist.
Needs to be a nice square cut.
Is this old tile just attached to the plywood?
Look around the room, is the grout all cracking?
When posting in forums, letting us know your location will help others give better feedback/advice/solutions to your questions