Subdomain with other droplet (Ubuntu+ Nginx)

I need to use 1 droplet for 1 service. I have 2 service to serve.

You shouldn’t have to use two separate Droplets. You would just use multiple server blocks in your configuration.

server {
  server_name mydomain.com;
  access_log logs/mydomain.access.log main; 

  root /var/www/mydomain.com/htdocs;
}

server {
  server_name server1.mydomain.com;
  access_log  logs/server1.mydomain.access.log main;

  root /var/www/server1.mydomain.com/htdocs;
}

Create two Ubuntu 14.04 droplets, follow How To Install Linux, nginx, MySQL, PHP (LEMP) stack on Ubuntu 14.04 | DigitalOcean on both, and then set up your DNS records accordingly: How To Set Up a Host Name with DigitalOcean | DigitalOcean.

Your DNS records should look like this:

@          A first droplet's IP address
server1 A second droplet's IP address