Typically, you would be chopping fresh rosemary up with a knife after pulling the leaves off the stem. Otherwise, I would use the mortar and pestle to bruise it to get the essential oils releasing.
Spice mills should only be used for dry! Processing "wet" ingredients will potentially make a paste; in that case, you'd do better to use a food processor as you'd probably be adding a liquid like oil.
I forgot to add that you could do the fresh herb in the spice mill if you are processing it with salt to make a rub. The salt will help keep it from sticking to the mill. Just keep in mind that you now have a lot of salt you plan to put in the food.
Since many of us are trying to lower sodium, finishing with salt instead of cooking with it is slowly becoming the new normal (except on TV and food blogs).
I think it depends on how you're using the rosemary, but I typically just mince it with a knife.
I like to use kitchen shears. I strip the rosemary leaves into a vessel of some sort and snip away.
A knife would be the most common, but it takes practice to mince herbs. My mother used to do the scissors thing, worked pretty well for her. But fresh rosemary actually contains very little moisture, I think that with care you could get it done in a mill; it would help if there's something completely dry you could mix in. Worth a shot, anyway.