For us a grandchild in need of some spending money has been the solution this year
He cleared 8 acres of spear thistles in 4 days - what a star
You don't specify whether it's spear or creeping thistle you have Muc. For creeping thistle constant mowing or grazing throughout the growing season for several years will
almost get rid of them. For spear thistles, you must dig out the whole root just before the flower opens. This way the plant has finished for the year but has not set seed (but if you leave the plants lying around the seed heads will continue to ripen). We modified a cheap spade by grinding down the sides to make a long narrow digging tool which is ok on softish ground. This year our ground is like rock, so we've been using an ordinary sharp spade and making a cross by the root to loosen it before lifting (with thick tractor drivers gloves, handling them by the lower stalk which is bare). We are still left with tiny rosettes around the place ie new seedlings and we will try digging those out by hand too, being careful not to leave the tiniest bit of root.
In the past we have not been sufficiently thorough in removing thistles and they come back each year - just miss one and let it flower and you're back to square one. Fence lines are especially difficult and behind hedges.
Our sheep love spear thistles because they are juicy and contain trace elements brought up from the depths. It's amazing how carefully they can eat them without spiking themselves but if they do then the skin damage can let in the orf virus
We have never used a chemical on the ground here and we are hoping that an annual battle of hand digging will eventually win the war