Do antibiotics effect the effectiveness of mirena (levonorgestrel)?

Not really: Mirena (levonorgestrel) is a progesterone-secreting iud (intrauterine device). The Progesterone is distributed systemically through the body and is metablized by the liver. Some drugs, including antibiotics can speed up the metabolism of the progesterone, but this shouldn't decrease it's effectiveness. Theoretically, you may get spotting. It also acts to prevent implantation, which is not affected by antibioti.

No: The Mirena (levonorgestrel) iud works as a contracpetive primarily by its presence inside the uterus. The progestin enhances the effectiveness (99%) and also gives the benefit of lighter periods. Antibiotics that might affect the processing of oral contraceptives (hormones) have no effect on the progestin from the iud because it's already inside the uterus where it works.