Hi Judith,

Mint does possess insecticidal properties, but the formulation makes a big difference. Japanese beetles do not like to eat mint, having a large enough stand may repel them from the immediate area. Sprinkling ground up mint leaves may have a mild insecticidal effect for a day or so. But peppermint oil is the most effective. And like many essential oils, the oil needs to make contact with the beetles to be effective. It also requires frequent reapplication, because it breaks down very fast with exposure to light/heat/water/etc. 

If you want to use mint to control Japanese Beetle, I recommend buying formulations that are already made. At home or DIY mixtures often don't have the right concentration to achieve beetle mortality while also avoiding damage to plants. There are also many other insecticides derived from natural ingredients that are much less harmful to the environment than conventional insecticides. They are called minimum-risk or OMRI insecticides. 

Let me know if you have further questions.