If the original tree was lost to borers, it is likely that the regrowth will as well, but in some time. But mimosas are very resilient, and put up with a lot. That old stump has a huge root system and is using it's big supply of stored nutrients to put out top growth. If you want to keep the tree, the best thing to do it to cut back o one new 'trunk'. Find a straight, healthy-looking stem and cut the rest off as low as possible. You may want to find a stem which emerges on the other side of the stump than the sidewalk's on, for obvious reasons.
This one stem will need to be staked, or it will tend to lean. Use 2-3 stakes, and don't tie the tree too tightly, or wind the string/wire around it; instead, put a protector (like a segment of hose, for instance) on the part of the wire that will be up against the tree. As the tree gets older, you're going to want to keep the tree's crown up above head level. You can usually take 1/4-1/3 of the top growth off from the bottom each year, until the crown is about 7 feet up. Mimosas branches usually arch, so that should be good for quite some time.
Expect suckers from the base to be a constant problem on this tree, and cut them to the ground whenever it's convenient. The rest of the pruning should be done when the tree is actively growing, so it can heal over quickly. In the spring after active growth starts is usually best, because the spring wood grows very quickly, and you can still see the branch framework fairly well (versus midsummer pruning).
What I personally would do is kill that stump and start anew with a higher quality tree. You would have to kill the old stump, which may take a while, and you may not be able to get it ground out properly with that proximity to the sidewalk. You could drill holes in the stump and carefully fill them with concentrated glyphosate. If you do choose to get a new tree, find a species that is resistant to pests and diseases that are the most common in your area.