Problems  with mimosa trees (Albizia julibrissin) unfortunately, are very common in our area.  They are beautiful, but fragile here.  In other parts of the country they are considered invasive.  Here is a link to information from OSU on them. http://oregonstate.edu/dept/ldplants/alju.htm
Your tree appears to be infected with a fungus, which probably means that the affected limb is dead.  You can wait until the tree leafs out to be sure, but if it is dead, it needs to be pruned out.  The fungus may have infected more of the tree, but that's difficult to say.  To pursue this further, please send us pictures of the whole tree and close- ups of the lesions.  Perhaps even better for you would be to take a sample of an infected branch into your Master Gardener office http://extension.oregonstate.edu/benton/.