Magento on DigitalOcean server

I dare to assume that the issue is caused by the lack of mysql settings optimization. The point is that without optimizing mysql, you won't be able to improve website speed, as mysql won't be using 100% of server resources.

These are the basic settings for 2Gb droplet (/etc/mysql/my.cnf):

key_buffer=32Mquery_cache_type=1query_cache_limit=1Mquery_cache_size=32Mtable_cache=128innodb_buffer_pool_size=256M

As these are the basic settings, you can use the app http://mysqltuner.com/ for further mysql optimization.

UPD:

As I can see from the results you got with mysqltuner, you need to experiment with the following settings:

skip-networkingquery_cache_limit = 4Mquery_cache_size = 256Mthread_concurrency = 4table_open_cache = 4096innodb_buffer_pool_size = 512Mjoin_buffer_size = 1M

Also note that after changes are made to the my.cnf file, don't forget to restart mysql

sudo service mysql restart

After settings are applies, test your website for some time, and then launch mysqltuner to see the results.

I use that exact Digital Ocean configuration (in terms of RAM and SSD - mine are on Centos and with the default PHP.ini config) for various Magento development/staging sites, they work fine so I'd say your server config is not the issue. It must be inefficient code in either a template or module.

I'd start profiling for it;

https://www.nublue.co.uk/blog/using-magento-profiler-to-speed-up-magento-performance/

I still use the AOE profiler module, it makes life easier I think;

https://github.com/fbrnc/Aoe_Profiler

I would also run n98-magerun to see if there are module conflicts;

https://github.com/netz98/n98-magerun

Then if you still can't find it switch to the default theme and start disabling modules to see which one it is.