Where do you put it

When weeding really thick stuff and you got loads of soil & compost matted in with the roots. What do you do with it? 
I don’t want to put it on beds because the weeds will just grow. Can’t put it in compost because soil won’t compost down. Again weeds will probably grow unless in a hot composter. 

Clumps like this, if anyone isn’t sure what I’m on about   .

         

I’ll get lots of stuff like this when taking all turf off. And big mats of weedy compost when emptying fish boxes.