MySQLdb
is mostly written in C which pypy can't use directly. You'd need to patch and recompile it.
The easier solution would be to use a pure python mysql connector library, like pymysql or mysql-connector-python
pymysql can even be used as dropin replacement for MySQLdb, all you need to do add:
import pymysql
pymysql.install_as_MySQLdb()
or put this in a module MySQLdb.py
, after that code which imports MySQLdb
should work normally.