Backup via mysqldump. Is this safe to do on production or will it crash the server?
Unless you add --single-transaction and you're using innodb tables this could block writes to the database for the period of the dump. So use --single-transaction (and innodb).

The only risk is if you are using a DO instance that is far too small and causes the mysql server or mysqldump (less likely) to run out of memory.

If you start gaining swap usage during the dump you can kill off the mysqldump process.

These few cases aside, its pretty safe.