Domain mapping is not done free of charge. When you purchase a domain name elsewhere and want to use it to map to from a WordPress.com blog then you have to purchase a domain mapping upgrade here at WordPress.com every year for $13. per year. http://en.support.wordpress.com/domains/map-existing-domain/
In order to map to a domain one must have an underlying .wordpress.com subdomain blog to map from. If you have registered a .wordpress.com blog you log in as Admin under the exact same username account that registered the blog and purchase a domain name by purchasing an annually renewable domain mapping upgrade for the blog.
If you do not wish to use that domain name here at WordPress.com then you can cancel the upgrade and get a refund.
Provided you are logged in under the same username account that purchased the upgrades, you ought to be able to request a refund from your dashboard > Store > My Upgrades
WordPress.com provides a 30-day refund on all upgrades except Domain Registrations, Domain Renewals, http://en.support.wordpress.com/domain-mapping/cancel-domain/ and Guided Transfers.
Note: It takes from 1 - 2 weeks for the refund to be received.