If it's green with leaves and buds, it will grow into a nice tree over time.
If you want to halt the new growth, you can cut the new growth down to the base single branch and tie a piece of cloth over it right at the cut end. Soak the cloth in a salt brine. Make the brine by heating water and stirring in amounts of salt until it is very salty to the taste, let it cool and soak the cloth. Usually a 4" square is enough but adjust according to the branch / shoot size. That will kill that particular shoot.
That method also works well with shoots coming up from the ground. The brine does not seem to affect other nearby plants if you don't spill it (thus just wet cloths).
To kill the stump dead, assuming it's cut flat across the top, drill a number of holes with a wood bit a half to one inch in diameter, maybe 4 to 6 inches deep. You might want to start with a smaller diameter bit if the going seems hard.
Fill the holes with gasoline, and let it soak in. You don't have to to anything else, no repeat necessary, no lighting anything on fire. Especially the lighting on fire part. It will kill the stump, the wood will rot over winter, next spring you can just dig out the stump.
If gasoline scares you too much or attacks your environmental sensibilities (or your wife's) you can substitute turpentine, which comes from trees so there's your argument for it's "green" qualities. But I found it takes longer for the stump to be ready to be removed with turpentine.
The Arborist might object to the above, the farmer won't.