What do you mean by heavy pruning?

I will be removing the top 1'-2' of very thin shots which have grown straight up off of the main frame of the tree. A local nusery person suggested I remove all of the growth which has grown straight up off the horizontial branches. Some of these verticial shots are 1"-2" in diameter.

We have one to in our yard. The wife hates is so we're doing some "REAL" hard pruning this fall. All the way to the stump!

You should have no problem with the timing. Epicormic growth (water shoots) should be removed completely, in my opinion, but I realise there are other opinions. There are causes to consider as well so you need to inspect the tree for disease but it may only be that the tree is open in the middle.

The common scenario is [crab]apple mowing, wherein the tree is overpruned and responds by throwing up a forest of verticals, which are then cut out year after year in an attempt to force the tree into a stereotypic caricature instead of a naturalistic, attractive specimen. However, crabapples may also throw up vertical shoots as a natural part of their development. Those in suitable positions can be left in place to gradually bend over and become twiggy and floriferous, others can be pruned out--although expect many of these to put up a fight (re-sprout).

We have a 14 tear old "flowering" crabapple tree that has a ton of fruit on it every year. The fruit is not edible.

Is there any way I can stop the tree from setting fruit in the future?

I have a three-year-old crabapple. Branches begin about 30" from the ground. Should the tree be pruned? To what shape and how? Where can I find a link with specific instructions about pruning?