Not only is this a molecular biology question, but also it is already based on false assumptions. Your first sentence already is false, miRNA doesn't bind to mRNA, but a programmed RISC complex does. Binding of miRNA alone is pointless. Therefore, I will close this question, first for the reason that it is off-topic and better asked elsewhere: Website for other biology field similar to Biostar and second because it is ill-posed and cannot be answered. So, I propose to read up the basics, e.g. the wikipedia article http://en.wikipedia.org/wiki/MicroRNA (even though this article might in fact contribute to the false assumption, because it doesn't mention RISC in the Introduction, also it assigns Dicer to the RISC complex).

Here is a recent review paper: http://www.nature.com/nature/journal/v457/n7228/full/nature07755.html