As we know, the private db_links can be dropped only by the owner of the database_link.  But you don’t have the password that db_link owner, then there is a workaround for that.

SQL>select * from dba_db_links where OWNER='SCOTT';
OWNER DB_LINK USERNAME HOST CREATED
------------------------------ -------------------- ------------------------------ -------------------- ---------
SCOTT LINK1 SCOTT testdb 04-NOV-11

SQL>drop database link scott.LINK1;
drop database link scott.LINK1
*
ERROR at line 1:
ORA-02024: database link not found

Now create one procedure under scoot user:

SQL> CREATE PROCEDURE scott.drop_db_link AS
BEGIN
EXECUTE IMMEDIATE 'drop database link LINK1';
END drop_db_link; 2 3 4
5 /

Procedure created

SQL> exec scott.drop_db_link
PL/SQL procedure successfully completed.

SQL> select * from dba_db_links where OWNER='SCOTT';
no rows selected