Q.Mock orange bush with briar tubers in the roots…..
I have a very mature very old mock orange bush that is “infested” with thorns from a “vine” of thorns that grow from huge tubers within the roots of the mock orange bush. How can I safely remove the tubers or otherwise kill the tubers without killing the mockorange bush? Other tubers of these briars were in a bed with azelias also entwined in the roots. One of the azelia had died…. When I dug it out I found the tubers some of which were 12 in long and 6 in wide and maybe 1.5-2in thick. I’m thinking what I need to do is completely dig up the mockorange, dig out all the briar tubers and replant the mockorange ( after cutting it way back…. To about five feet) do you agree?

If you decide to transplant your Mock Orange, doing so when the shrub is dormant is recommended.
Here are some articles to help you.
https://www.ehow.com/how_8757112_transplant-mock-oranges.html
https://www.gardeningknowhow.com/ornamental/shrubs/mock-orange/mock-orange-bushes.htm
Do to the size and the issue of the invasive briar vine, you don't really have any good solution.
You could cut the vines down to the ground or tuber, and paint the cut ends with full strength herbicide.
You would need to be extremely careful to not touch the Mock Orange with the herbicide.
I personally might try a test of this method, before transplanting.
This technique is covered in these articles.
https://www.gardeningknowhow.com/ornamental/trees/tgen/kill-zombie-tree-stump.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/weed-trees.htm