When having mirena (levonorgestrel) for several months is it normal to have brown discharge?

Not usually: It is a possible side effect. It doesn't happen commonly, but prolonged, irregular bleeding can be a side effect. If it is a new symptom, you may want to have a sonogram to ensure it is in the right place. If so, then sometimes a short course of birth control pills or some supplemental estrogen can stabilize the bleeding. Also good to make sure u weren't exposed to any stds.