I think I found what is causing slow send rate. And you're right @underthegun, it's kind of related to MySQL. But I believe the issue is with Sendy itself. I might be wrong.

Something I observed with MySQL was that it's writing temporary tables to the disk.  This is reported by MySQL tuner.

[!!] Temporary tables created on disk: 80% (173K on disk / 216K total)

This is not ideal. Writing to RAM is much faster. There are few reasons for these disk writes. Following is a quote from DBA answer, 

Temporary tables are created on disk when:

• TEXT or BLOB fields are present (because MEMORY doesn't support these types)
• the size of the resulting implicit temporary table exceeds the lesser of tmp_table_size or max_heap_table_size
• If a column w/ more than 512 bytes is used with either a GROUP BY or UNION or ORDER BY

Will be playing with these for next few days.