Hello Stamel.
Yes, slugs are a problem under mulches of straw and less-decomposed materials.
So to be clear of the weeds you needed to have raked or hoed them when small, or use a trowel to scuff the surface and disturb them so that their roots dry out on any day of sun and wind.
But maybe they are now too big for that, so the best method is to pull them all out, then to put them on your compost heap. Weeds pull out easily from the surface compost (whether it is originally from cow manure or whatever) and after pulling them you will be impressed to have a clean surface quite quickly, without adding any more mulches.