There are two types of thistle we tend to get in pasture, sometimes three. There's spear thistle which is the big very spikey one with large deep purple flowers which grow as individual plants and are spread by seed. Then there is creeping thistle, much smaller and more slender, with small pale blue, sweetsmelling flowers beloved by honey bees. These spread by underground roots which go on forever in a network, so they tend to form large areas of infested pasture. Last and least is cirsum rivulare which has small darker leaves, purple flowers and grows in clumps. It is also sold as a garden plant, and is the easiest to eradicate by pulling.
Spear thistle should ideally be dug up when the flower spike is up but the flower has not opened. If after digging you dump them in a heap then the flower bud will still open and seeds will form. By digging then, even if you don't get the whole root there will be no strength left for regrowth (you hope). Spear thistle has a long tap root, which brings many minerals to the surface, is, amazingly, relished by sheep, but will deplete your pastures when removed.
Creeping thistle can be controlled more easily by frequent close mowing, several times a year,and it's best to collect the mowings especially if you have sheep, as the fleece will pick them up.
If it's spear thistle you have then the idea of hand digging 15 acres is beyond dedication, but we have been removing ours by hand from 9 acres for the past few years. The first year we dug three huge piles and burnt the lot, this year we have only found three wheelbarrowsful, so we're gradually getting there. We eradicated ragwort over a few years by the same method, although the occasional seed floats in. Hand digging spear thistle is a skill (which I've made sure I'm bad at
) as you have to get all the root out. We have had no success with cutting, only digging.