So my starter has died on my Riding Honda Harmony 1011 mower and for the life of me I can't figure out how to remove the starter, never mind replace it. Seems as though you need to remove the fly wheel to get to the starter bolts, but I can't get that off. Am I missing something simple or do I not have the right tools?

Hi,
Most Honda engines do require that. A very few have recesses in the bottom of the flywheel that allow the bolts to rise up into them for removal.
If you can get the nut loose, you can get the flywheel loose with out damage with a pair of hammers (not claw.) Thread the nut up flush to the end of the crank. Place the face or ball of one hammer on the tip of the crank and strike the other end of that hammer with the second hammer. I use a large ballpein hammer and a 2 lb double-face (flat) as the second.
Never strike the flywheel itself or you risk dislodging the charging magnet.
Link to a parts breakdown of an engine similar to yours is:
http://cssportal.css-club.net/honda/pp-service/data/13Z1F401.pdf
Right size/family, different model.
Peace,
Clarke
PS Did faint at the price?