How much can I trim my Japanese Maple without harming it?

If you look at the outer portion of the canopy, you will see that these are normally dense and little sunlight penetrates them. I always advise people to thin the outer canopy and allow sunlight inside so that you retain the interior and lower branches. Thinning and reduction can be done at the same time if you take your time and are selective. Your cuts shouldn't be any bigger than 3/8". Don't remove any interior tissue unless its dead.