Just cut off the flower....no need to cut the stalk....just cut the flower and the seed pod off at the base.
with a day lily you will want to remove just the bloom while there are still other blooms to bloom on the scape.
Leave sunflowers....the birds love the seed heads and they won't continue to bloom.
Larkspur just cut off the individual bloom stalk. Oleander just snip off the dead bloom.
Linda C