I would try first inspect your Droplet's CPU and memory usage. Try using htop - an interactive process viewer for Linux.

So you can find out if you're running out of memory (causing swap) or too much CPU processing (and what is using that resources).

http://hisham.hm/htop/

I run top command from shell. Here's the i got;

[root@s ~]# top
top - 12:45:50 up 1 day, 5:31, 1 user, load average: 5.34, 5.40, 5.58
Mem: 1020388k total, 880792k used, 139596k free, 61336k buffers
Swap: 0k total, 0k used, 0k free, 413648k cached

PID USER PR NI VIRT RES SHR S %CPU %MEM TIME+ COMMAND
20437 mysql 20 0 1048m 189m 7232 S 73.2 19.1 704:47.40 mysqld
6701 apache 20 0 510m 20m 9236 S 1.3 2.0 0:00.26 httpd
1139 admin 20 0 509m 21m 10m S 1.0 2.1 0:02.30 httpd
4008 apache 20 0 508m 20m 10m S 1.0 2.0 0:01.31 httpd

Looks like there's quite a bit of load on the CPU. Try upgrading to a plan with more CPUs—does that help?

Thank you so much.

Looks like most of CPU usage is from MySQL. From this point you can consider analyzing which queries are taking too much time to run. Also, you can migrate just MySQL to another, larger server (you will get more CPU cores for the price).