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I don't know of anyway to stop them. I have the same thing on roses and citrus trees.

I am waiting for the rain to stop so I can cut off the root suckers from my Satsuma. No way to stop them other than pruning.

We have found over the years that you get a better control over both water shoots and suckers if you can rip them from the tree by hand. There seems to be a slower return growth from this than by cutting.
Plays hell with your hand though!

pruning in june, after the first flush of growth has happened, discourages regrowth much more than winter/dormant pruning...

Is there a way to successfully divide and save a root stock sprout if it is growing on the root about a foot away from the main trunk?

I ask because I practiced grafting on some of those, and one of the Enterprise grafts survived and is taking off... At the foot of the Enterprise tree....

The only way I know Star is if the root it is growing from is small enough to devide off itself.
Just as you would from a stool bed.

Applestar - since you are taking a shoot from the root stock I suppose you could root it and use it as root stock for cuttings from the fruit bearing portion of your tree. You are cloning the root stock.

An interesting idea.

Well, actually, what I did was graft a scion from Enterprise to one of the root suckers (water sprout?).

A couple of years ago, I was practicing a grafting technique and was inspired by a video for avocado grafting that said best time is when the root stock is in vigorous growth, and I looked over at the root sucker and thought -- "Hmm... THOSE things are REALLY vigorous...."