Although there are multiple medications, including many antibiotics, that can decrease the effectiveness of oral contraceptives, such as Yaz, the same does not hold true for intrauterine devices like the Mirena. Basically antibiotics decrease the effectiveness of oral contraceptive pills because the affect the way the liver breaks them down, which can result in blood levels of the contraceptives that are too low.
However, the Mirena, as an intrauterine device, primarily works by being physically present in the uterus, which prevents pregnancy. The Mirena device also does have hormones in it, which modify the uterine lining and decrease spotting and menstruation over time. However, this is a back up function, and the intrauterine device would work just fine even if it did not have the hormones in it. In fact, many older intrauterine devices (such as the copper or Paraguard device) did not have any hormones in them and worked just fine.
I think you can feel confident to take the full dose and course of the amoxicillin that you were prescribed without worrying about potential effects on increasing your risk of getting pregnant. As always, if you have any more questions about your intrauterine device or contraception
in general, feel free to talk to your primary care doctor