Yes, overwatering will prevent the roots from growing properly, making them unable to support the top growth. Also, wet soil like that can cause roots to rot, creating the same result.
Water the plant after it has been repotted, but don't water again until the surface of the soil is dry. In fact, it would be good to dig your fingers into the soil to test the dryness. Water when it's dry about an inch down.
I suggest that you repot the plant in fresh soil. Remove any of the old soil that comes away easily, but it isn't necessary to remove a lot of it. Don't feel that you have go wash the roots clean, for example. You can repot it in the same container, if you like, or a different one. Don't use a larger one, though.
Make sure the container has plenty of drainage holes. If the container is in a saucer or other tray, be careful never to allow water to stand in it.
Mimosas do like moist soil, but not soggy soil, so you will want to adjust your watering schedule to prevent future overwatering. You can add some perlite to the soil mix to help it drain more rapidly, as well. An unglazed clay container, rather than one of plastic, can also help prevent soggy soil.
Never hesitate to gently remove a plant from it's container to check the condition of the roots. It does no harm, and can resolve many problems with the plant's health.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams