Remote Mail Exchange Server not Working

I am using the mandrillapp.com mail provider to send mails vith smtp protocol. I have edited both mx and spf records to send via this e-mail server. I have also changed the Email Routing to remote mail exchanger. However when I try to send mail on server, the server still tries to send e-mail locally. On the other side, I can easily send e-mail from my local machine.

Here is the output of error I get:

Code:

SMTP -> FROM SERVER:220-**local server** ESMTP Exim 4.84 #2 Wed, 17 Dec 2014 11:19:17 +0200 220-We do not authorize the use of this system to transport unsolicited, 220 and/or bulk e-mail. 
SMTP -> FROM SERVER: 250-**local server** Hello **local server** [**local IP**] 250-SIZE 52428800 250-8BITMIME 250-PIPELINING 250-AUTH PLAIN LOGIN 250-STARTTLS 250 HELP 
SMTP -> FROM SERVER:220 TLS go ahead 
SMTP -> FROM SERVER: 250-**local server** Hello **local server** [**local IP**] 250-SIZE 52428800 250-8BITMIME 250-PIPELINING 250-AUTH PLAIN LOGIN 250 HELP 
SMTP -> ERROR: Password not accepted from server: 535 Incorrect authentication data 
SMTP -> FROM SERVER:250 Reset OK 
SMTP -> FROM SERVER:250 OK 
SMTP -> FROM SERVER:550 SMTP AUTH is required for message submission on port 587 
SMTP -> ERROR: RCPT not accepted from server: 550 SMTP AUTH is required for message submission on port 587 

See, still tries to send mail locally.