Can an agent drop a specific conference participant?

For a UCCX deployment, there is not a way for an agent to drop a participant from the call using a Finesse API.

For a UCCE deployment, it is possible for an agent to drop a participant from the call using the Dialog-Drop Participant from Conference API. 

This API allows an agent or supervisor to make a request to drop other participants from a conference based on the permission set by the administrator. By default, this API is only available for supervisors, but the administrator can use the Finesse CLI to expand access to conference controllers or even all agents. This setting is reflected in the enableDropParticipantFor property.