From UIM document on restfull calls Delete a Contact(Single), REST calls are made on uri: /contacts/{contact_id} with method 'DELETE' to drop a particular contact user.
For the call to be successful, caller needs to known contact_id.
Environment
Release: Component: UIMWSR
Resolution
Currently there is no way to get contact id of a contact user via REST calls, instead try to run the query to table in CA_UIM database:
To get a contact user by name:
SELECT * FROM CM_CONTACT WHERE login_name like '{contact_user_login_name}';
To get all contact user details:
SELECT * FROM CM_CONTACT;
Then you can make a REST call to drop this contact user with contact_id returned.