Transplanting always involves some amount of root loss and damage. Try to minimize the impact by careful digging (and by having the new hole mostly ready before you uproot and transport the tree).
I’d cleanly cut the root near to the house, with a sharp shears.
More than the single root being severed, the plant will react more likely to being uproots over all, and may sulk. Keep it well-watered (not drowning, not dry) and do not feed (big mistake after uprooting).