Well, that's weird! It might be that Steam is restoring the save file through Steam Cloud even though you deleted it... could you try doing the same but with Cloud disabled for the game?
To disable Steam Cloud for the game, go into your Steam Library, right click the game and choose Properties. Go to the Updates tab and make sure the Steam Cloud checkbox at the bottom is unchecked!
Then go back and rename arcademode.sav to something else and try going into Arcade Mode again.
If it still doesn't work, could you try going into the %APPDATA% folder and renaming the whole "Secrets of Grindea" folder? This will of course give you a complete fresh restart, but I'm interested to see if that solves your issue or not.