There is no way to delete a save, the way you could do it is just deleting a reference to a save, like checking a webstorage value that would be related to that save.
Ashley the request is still really valid, could a simple "delete existing save (by name)" exist?
you can delete the savegame by "clear cache" of your browser... and this isn't good if you want to make a game online...
but it depends what do you want to store... save game system will save all, position of the instance, variable, global variable etc...
for delete a savegame is possible to save a state at the first access like "reset" savestate, and when you want to reset all stats, just click a button, and a "reset" savestate will replace the old gamesave... that should work...
but I suggest to save a game on some server with a php an AJAX, and if the player want to reset the game, just do this process and replace with the json file on the server... I don't like to store information on the browser... if you are making a game with a lot of level, or something important to continue the game (store coin, jems, position of the sprite...levels..other important stuff..)....and the user clear the cache, just say bye bye to your save...
but depends of the game... if you are making a game like tetris... and just post your score at the end of the game... no problem
EDIT: I add a capx