We use a 6' tiller and have had a 4' tiller on our farm for over 25 years. Virgin soil is tough to break down, so much root mass, dry conditions don't help.
My experience is run over the ground at a higher speed to open up the root mat then let is dry for at least a a week. Follow with a more a aggressive cultivation, slower tiller speeds, disc, or chisel plow. Let the field dry out again then finish with tiller.
Tillers are best to finish a field. Not the best tool for initial cultivation.
Its rare we slip the clutch, sounds as others have suggested, tool adjustment is needed, or you have a defective clutch.