Canada thistle is one of the toughest plants to get rid of - ever.
It reproduced both by roots and seeds so tilling/disking can actually make it spread more. In my experience, there has been no natural products that make a dent on this weed. Repeated mowing (like 3-4 times per season) can weaken the plant and done for years on end can eventually eradicate it. If you have small patch you could try solarizing your soil but keep it covered for a couple years.
Depending how bad your infestation is, it is a plant which can warrant the use of herbicides. I've had success with mowing the plants down, and then using a foam paint brush to dab chemical directly on the stem. This is best done after your first fall frost since the plant is taking sugars into the root stock to store for the winter so the chemical directly translocates into the root.
I HATE HATE HATE HATE Canada thistle - and I don't use the H word a lot. In Idaho, it is actually illegal to have it on your property