There is no need to pull all the plants out and the only reason "weeds" grow in that bed is most likely because the soil is bare and Ma Nature does not like here soil bare so she plants stuff to grow and we call these "weeds". A good, heavy mulch will help control "weed" (a "weed" is a plant growing where we do not want it to grow) growth as well as aid in soil moisture conservation and aid in keeping the soil cooler so your plants will be happier.