Something is boring into my Mimosa trees

I have two 3 year old Mimosa trees, that are approximately 10 feet tall, and there is something boring into the wood. I don't know if it's on the inside boring out, or the other way around, but it's somewhere between 1/32 to 1/16 of an inch around, and it's leaving a 'sawdust' string hanging off the wood. it is just now beginning to leaf out, but the holes began before the leaf buds were visible. The outside cat(s) were using the trees as a scratching post this winter, so I don't know if something got in through the damaged trunk, or if this is common to the mimosa only. Please help!
Thanks - Mary

[MJDamiani]

I also have boring insects eating away at the base of my Mimosa tree. The bark is falling away at the base of the tree and there are small grub looking worms in the decayed parts of the bark. I was looking for some chemical to kill these parasites, I used Ortho Lindane in the old days, but a better solution must me available.