Mazal tov on the recent birth of your baby!
You may attribute the bleeding from the insertion of the Mirena (and any subsequent bleeding during the first few days) to trauma, and it does not render you niddah.
However, since Mirena releases hormones as well, some women experience continued bleeding even beyond the first few days after insertion. In this case, if you experience an actual flow of blood after the first few days, you are rendered niddah. If you only experience staining, you may take precautions against becoming niddah from staining by wearing colored underwear and waiting a few seconds (ideally 15 seconds) after urinating before wiping. Please see our pages on stains and toilet paper for more details.
Please feel free to get back to us with any further questions.
B’Hatzlacha!
This response has been updated to reflect the rulings of our current Rabbinic Supervisor, Rav Kenneth Auman, regarding waiting before wiping.