I've never taken a tyre and rim off, when changing tubes on similar mowers.
Grumpy has explained it well. Chuck her on her side and drive the bead inward with the end of a tyre lever (yes it sounds rough).
You might want a helper to keep the weight on the type when re installing it.
If you still don't have any luck, take the hole machine to your local friendly tyre shop they won't care that its still on the rim.
