Waiver Wire Technicality Question

Say I wanted to make a WW claim on 2-3 players ,but I was only willing to drop 1 player to make the acquisition from the wire.

Would my highest rated priority player if available be my only acquisition and then all remaining claims be cancelled(since the player I wanted to drop would therefore no longer be on my team) or would I continue to automatically drop my higher rated claimed players until all of my lower priority claims were honored?