Question
will mimosa tree roots hurt my septic tank

Answer
Any tree planted on top of a septic tank or the fill lines could cause problems. Tree roots seek out water so if there is a leak the roots will get in to the lines.  Do not plant a willow or maple anywhere close to a septic tank or leach lines, but just about any other tree inclined to plant would probably be just fine. There is an online Cooperative Extension Service Bulletin entitled "Planting on your Septic Drain Field" which may be of interest to you, so far as recommendations, etc. are concerned. http://www.ext.vt.edu/pubs/envirohort/426-617/426-617.html

Also, there are copper sulfate preparations that can be flushed into your septic system once yearly that will kill any roots that may have found their way in - and these preps do not have any adverse effect on the microbial population in your septic system, nor do they damage the trees.

Mimosa trees have a spread of about 10-20 feet at maturity so try to keep them away from the tank 10-15 feet. I would also use the copper sulfate treatment once a year as a prevention.