1. Go to "Websites & Domains" and select Databases.
2. Click on the "Copy" icon next to the database you want to copy.
3. There are two options there, if we pick "localhost:3306" from the dropdown which is shown in the figure below, data will copy to locally database server.
4. If we copy the backup to the remote database server then choose "other" option and give server ip address, Username and Password.
5. After clicking "OK" the database copying process will start immediately.
6. Once the copy has completed, you should modify your website's scripts, so they connect to the copied database, such as by modifying connection strings to connect to a new database name, username and password.