Japanese maple /roots
It will all depend upon how large the root it and how much other root capacity the tree has. If it is a small root, you can feel comfortable removing it, but usually it is the large roots that cause a problem.
You can send us a photo to help us better appraise the impact of removing the root. You can also have a certified arborist look at it. You can find one at www.treesaregood.org by following the prompts to an arborist near you. These arborists are certified by the International Society of Arboriculture and are the ones we recommend.