Mower is sputtering and then finaly shuts off will

Sounds like you may have water in your gasoline. Look in your gas tank on the mower with a flashlight or a pen light and see if there are bubble like globs at the bottom. Do the same with you gas can.
The best thing would be to get out the bad gas in the tank and put fresh gas in if that is the case.
The other thing you could do if you find you have water in it is to go dawn to the Auto or hardware store and buy a can of Heet or any other type of water remover. Try and run it and refill with fresh gasoline.

If the gas is good try and see if the spark plug cap is tight or even just take the plug out and give it a good look.
Another thing it could be is if your getting air in the gas line from a crack or if it is loose.