If you can't clean it by yourself, you can take your glasses frame back to the place where you bought them to have them cleaned. The worker there will use special cleaner to remove the stain. If he or she can't clean it, then you may buy a new one.
Alcohol may help you clean your dyed white glasses frame. Try rubbing alcohol with a soft cloth and then gently massage the stain on your white glasses frame until it's gone, which won't harm your glasses frame. I used to apply alcohol to clean everything and it does work.
You can try using nail polish to help get rid of the stain on your white glasses frame. You will find the nail polish at any boutique, which won't cost you much. Then apply a little nail polish on a soft coth and rub your frame with the cloth. The stain will be removed finally.
Here I suggest you to take it to your local eyeglasses store. they will use a kind of special cleaner to make the stain gone. Please do not clean it just by yourself, or it will damage your eyeglasses.