There are lots of ways to speed up your Magento’s database but the 1st way is always to clean it Logs.
Magento is very good, robust and highly stable eCommerce system but it’s database is not as efficient as it should be. Almost every operation with database for every user is written down into logs tables and sometimes these log tables have millions of records and take hundreds megabytes of disc space. Cleaning logs regularly helps in reducing latency of query execution and hence improves performance. Regular database cleaning can tidy up Magento database and all unused, cluttered or over encumbered records are sorted out.