I have a willow oak tree that I bought from a nursery, which was about 3.5 feet tall, but it had a lot of smaller branch growth near the bottom of the trunk that had not been pruned. I cut the top part of the tree off and left the smaller branches at the bottom to train into a bonsai. I left the tree in the original pot for a full season and then re-potted into a temporary container. When I re-potted I cut back the smaller roots, but did not cut the tap root. After two more seasons I re-potted again (to put into a decorative container), and trimmed the smaller roots some, but was afraid to cut the larger tap root. The tree looks great and is growing well, but is in a little larger container than I would like because of the tap root. I have a picture of the tree in the autumn before I last re-potted it attached. Would it be ok to cut off the large tap root during the next root trimming?

Hard to tell without seeing the roots. Normally it should not be a problem for a healthy tree. If you are unsure, you can always place a tourniquette around the toproot, just below the surface roots and remove the root a year later.