Yup, cut and use - don't waste those nutrients!
Grazon-90 will kill 'em off, yes. And the active ingredient will persist in the sheep's systems and their poo, in any hay made from the field and in the systems of any stock (including horses) fed that hay and their poo, and kill all non-grassy plants for years. All of which is maybe not a problem so long as no-one along the way uses any of that muck for other than grassland. It'll kill garden plants, vegetables, any sowed (non-grassy) crops, etc.
Oh, and it kills fish too, if it, or any of the poo containing it, gets into any waterways.