First off - never, ever allow any nearby thistles to go to seed. Second, like any plant thistles ultimately need to grow leaves for photosynthesis to produce food to survive. Continue to take away those leaves as they sprout and the plants' roots will eventually run out of their nutrient stores and the plants will die. You will know you are winning when the leaves start coming out of the ground yellowed and stressed. So, prevention and persistence is the organic method.

Chemical herbicide is the other method. For spot control duct tape a small paintbrush to a stick (so you do not have to keep bending over), put on rubber gloves, dip the paintbrush in a small bottle of herbicide as you go around and swipe a leaf or two of each plant. Kills 'em dead, no over-spray, ground contamination is minimized, and waste of expensive herbicide is minimized.

I use a combination of the two methods, depending on the situation (no herbicides in or near food production areas for me, period). Thistles do not intimidate me as much as they used to. I learned to never let them get big, and I also learned how to safely grab them and now go in barehanded to pull 'em out. When the young plants are pulled properly, they come out root and all. The young leaves have soft, immature prickers so they do not hurt as much if accidentally grabbed.

The one thing I never do is leave pulled thistles laying around. There is nothing more painful than unwittingly placing your hand on the ground where there is an old dried thistle leaf or plant, or grabbing one when doing garden cleanup. You will be pulling prickers out of your skin for an hour while using a magnifying glass. Real fun stuff.

Good Luck!