We viewed your photos.  This looks like damage by the ambrosia beetle. Take a look at our website for photos and more information. This borer is attracted to stressed trees. In general, trees can be affected by drought, poor drainage, planting too deeply, poor soils, soil compaction, etc. These factors make the trees susceptible to secondary issues like borers. Insecticides are ineffective against beetles that have bored into the trees. If the tree declines and is on your property, you will have to remove it.  

These beetles can have a wide host range so it is important to keep your other trees in good health.  Make sure mulch is no thicker than several inches and away from the base of the trunk.  Keep the trees well watered during dry periods.
http://extension.umd.edu/hgic/ambrosia-beetles-trees-and-shrubs

We do not recommend planting mimosa trees as they are invasive spreading by seed and vegetative means.  They are also susceptible to a wilt disease.  Take this opportunity to replant with a native tree species.

mh

The tree is huge, 12in at base, do I have to completely burn the entire tree to ash or just the outer inch?

Ambrosia beetles can get further into the heartwood of a tree, not just the outer inch. 
https://extension.umd.edu/hgic/ambrosia-beetles-trees-and-shrubs

ckc