I would suggest you to setup Replication in MySQL. You will have to setup a Master and Slave server. All read-writes to the DB could go to your Master Server.
The DB backup can then be taken from the Slave server without interrupting the Master. Even if you pause/stop the Replication process during the backup process, the Master wont get affected. Only the Slave will be affected during that time. But since the read-writes are directed to the Master, your website wont be locked out.
To enable incremental backups, with the Master-Slave setup, you will have to enable Binary Logging on the Slave too (Master will always need Binary Logging for Replication).
To do a secure replication, you will have to connect Master-Slave with an SSL connection.
You can find all the information here