Mmm you're right, there's no way to erase a saved game but you can overwrite it if you want. Try pressing ESC during the game and then saving the game in another saved game. It's not the best save system of the world so I'll rework it from scratch for the sequel and maybe add an auto-save feature too. Sorry for the inconvenience!
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There's 3 slots to save your progress. You can save multiple times in these 3 slots. Just press the Escape key during gameplay, then click Save Game and click any of the three available save slots. If you're having trouble saving your progress I strongly recommend downloading the desktop version, which saves a screenshot of each saved game so it's easier to keep track of your progress.