Apples often grow lots of suckers from the roots, especially if the roots are damaged.
Cutting off at ground level will only encourage more shoots from the base of the sucker. Digging down and remove at the source is the most effective way to remove these as Nozzle head has already said though they will often grow back later.
You can grow new trees from the suckers if you want to. They probably won't have their own roots yet but will often strike quite easy as cuttings. Even if there is just a tiny start of a root the sucker will be way ahead and should take quite easy when transplanted.
Starting with such tiny shoots will take many years to reach bonsai but can be rewarding if you have that patience.