Will the plants grow the tops back?
Not recommended, the plant puts out the stems from the tuber, if a strong type it may send out more shoots, but the potatoes will be weaker, plus you need to hill them to hide the new tubers.http://www.almanac.com/plant/potatoes
YES. Mowing down the tops of the potatoes will hurt them. If the tops grow back, it will be from energy stored in the potatoes. You want to maximize the size of the potatoes --- not make them smaller.
dumb idea. you should have been out there pulling weeds.