Yes, It is possible to kill a deer on a moped. It was once believed to be an impossible feat, but things have changed.
Heading back from the local grocery store, with some orange juice and a coke, we encountered a family of deer. We were riding our trusty mopeds and the baby deer (fawns) took off running. I yelled to my Puch riding buddy, "Hey look! I'm faster than a deer!" we experienced a moment of sheer bliss as, for a moment, we ran with the herd, weaving in and out of the joyful pack of wild animals. Then one of our newly found friends decided to take the high road, literally, and starting galloping on the road. We first thought of this as a playful stroll, but now we started to suspect fear in the minds of these young creatures. I thought this would be a perfect time to test out my horn. Apparently, deer are scared of such noises, and he veared to eh left of the rode, into a fence, and died.
Naturally we went back to take a photo to prove our story, but locals had already loaded it in the back of their truck and began preparing for dinner.