When someone is considering to take 2 drugs both of which can have severe side effects, he/she should discuss this with a doctor, so this part of the question CANNOT be properly answered here.
Mirena can actually cause acne:
1. Mirena side effects (Drugs.com)
The most commonly reported adverse effects are alterations of
menstrual bleeding patterns, nausea, abdominal/pelvic pain,
headache/migraine, dizziness, fatigue, amenorrhea, ovarian cysts,
genital discharge, acne/seborrhea, breast tenderness, and
Dermatologic side effects: Very common...Acne/seborrhea (15%)
2. Mirena (Drugwatch)
Common side effects of Mirena include:
- Weight change
- Mood changes
- Breast tenderness
- Ovarian cysts
- Vaginal discharge
- Abnormal bleeding patterns
3. Mirena safety considerations (Mirena-us.com)
Between 5% and 10% of Mirena users may experience:
- Depressed mood
- Heavy or prolonged menstrual bleeding
4. Mirena contains the progestin hormone levonorgestrel, which can increase the blood levels of free testosterone (androgene hormone), which can cause acne (AAD.org).
Stumpf PG et al, 1981 Changes in physiologically free circulating estradiol and testosterone during exposure to levonorgestrel (PubMed)
During treatment with d-Ng [levonorgestrel]...the % of testosterone
increased to about 55% of the total.
5. There are many conflicting anecdotal reports of the effect of Mirena on acne online.