You can take a piece of downspout, cut a piece out of the top of it to create ears, then screw those ears to an elbow mounted on the bottom of the existing downspout. Then you can fold the extension up when mowing. Bonus points if you make a little hook out of the cutout and screw it to the side of the downspout high enough to latch the extension when it's folded up.
Like this.
Or this