If you are digging up a tree that was planted by a squirrel and it’s about two years old, you have take into account the water balance between the roots and shoots.
If you cut and remove a lot of the tap root, you will be losing the moisture it would normally be pulling from the ground. For example, if your surface soil is extremely dry and the tap root had to grow very deep in order to reach the water table, cutting the tap root can cause significant wilting.
If you have been irritating this tree, there are probably a lot of feeder roots near your drip emitters or sprinklers and if you can keep these from being damaged too much, your tree should be ok.
When digging up a tree, I like to give it some vitamin B1 several days or a week before digging it up.
Also, when you dig up a tree, try to notice how much of the root system got destroyed. If you cut off or damaged 30% of the root system, you may want to consider pruning the trees canopy by about 30% or so in order to balance moisture loss.
Also, after digging up a tree or removing an air layer, you may want to consider putting the tree in mostly shade or only very partial sun for about two weeks depending on how much transplant shock is visible. You will then have to acclimate it to full sun again.
Simon