I'm a bit confused as to which type of thistle is the problem. Spear thistles are the tall 'Scotch thistle' things with very large flower heads which spread by seed dispersal and grow up from a single rosette; creeping thistle is the kind with much smaller leaves and flowers which spreads everywhere by root spread as well as seed.
For the single tall spear thistles, you're best to wait until the flower stem is well up, then dig the whole plant up and burn it. The seed heads will continue to ripen and disperse if you leave them lying in a pile. It takes several diligent years of removal, including that secretive plant which manages to miss your attention because it's hiding behind the barn. If you try to remove the plant before it's developed the flower head then it tends to send up three to replace the one. Best to let the plant expend its energy on producing the flower stalk and bud, but not to open the flower, before chopping it. We have controlled 9 acres with this method and now have only the occasional one popping up. Too labour intensive for a larger area.
For creeping thistle, frequent mowing throughout the season will gradually wear it out, using a topper or even a lawn mower if the area is small.
Sheep will happily graze both types of thistle, and song birds love the seed (same as niger seed which people spend a lot on importing for gold finches

)
There's also water thistle (Cirsum rivulare I think it's called) which has a deeper purple but smallish flower head. I think they are pretty much the same as spear thistles and spread by blown seed.