Answer: I think the answer to your question depends upon a lot of things. First, the shrub you are planting should be at the same finished soil level as it was growing in the nursery pot. So, set the pot into the hole to check and make sure the hole is not too deep. Next - if you did not damage the root when digging, it will be safe to plant your shrub in the hole along with the exisiting root. The part of the tree root you uncovered is busy extending itself. The new growth at the end of the root is where it will be searching for food and water. While the part of the root you uncovered will continue to grow in girth, it won't be taking up moisture and nutrients to an extent that it will bother your shrub. And, plant roots of all kinds live happily together underground without too much trouble. (Think of stands of trees in the forest or the way bamboo rhizomes spread underground.)
If you cut off the offending root it probably won't hurt the tree. Instead, the tree will probably develop a forked root at the cut site to make up for what it has lost. This may or may not be a problem for your shrub. However, in response to having one of its roots cut off, the tree may begin sending up suckers or upright shoots into your yard. So my advise is to leave the root alone, plant your shrub at the proper depth and allow them to figure out how to get along underground.
Best wishes with your landscape!
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