Yes, but it depends on your goal.
Cutting the flowers after they've faded or died will encourage the plant to produce more blooms because the plant then has to produce more flowers in order to eventually go to seed and thus produce more flowers next year.
If you want more blooms: Deadhead (cut off spent flowers) through summer to encourage the plant to keep producing new blossoms. Snip the stem just above a set of healthy leaves or side shoots.
If you want wildlife benefits: Stop deadheading in late summer. The dried seed heads are loved by birds (especially goldfinches) and add winter interest to the garden.
If you want natural reseeding: Leaving some seed heads in place allows coneflowers to self-sow, giving you new plants next year.
To deadhead coneflowers, cut just above the first set of leaves. Then cut the plant back to keep it compact.
One approach is to deadhead early in the season for more flowers, then let the last round of blooms fade naturally for the birds and seeds.