This is how I remember the version heard on Dr Demento's show:

I'm looking over my dead dog Rover,
That I over-ran with the mower.
One leg is missing the other is gone.
The third one is scattered all over the lawn.
No need explaining the one remaining
It's splattered on the kitchen door.
I'm looking over my dead dog Rover,
that I over-ran with the mower.

And a second verse I didn't remember (found on the Boy Scout Trail website):   

I'm looking over my dead dog Rover
Who died on the kitchen floor.
One leg is broken, the other is lame,
The third leg is missing, the fourth needs a cane.
No need explaining, the tail remaining
Was caught in the oven door.
I'm looking over my dead dog Rover
Who died on the kitchen floor.