Kosk, I had a problem with Canadian thistle when we first moved here - our front field was absolutely overrun with it, we didn't have good enough fencing for livestock (who don't eat it anyway), and we didn't have a field mower at the time. Our neighbors kindly took turns mowing that field just to keep the infestation from moving into their fields. It took a couple years, but eventually we won that battle. I think the key to thistle eradication is to not let them go to seed and to continue to cut them back to the ground. Eventually the tap root will die out. The seed remains viable for a couple years, so be diligent.
What variety of thistle do you have?