That is possible and one method of doing this is:

First stop mongodb
sudo service mongodb stop

Move your database to block storage. (Depending on the version, your database may be in a different location. Check your MongoDB config file for dbpath option.)
sudo mv /usr/local/var/mongodb /block/storage/mongodb/

Create a symlink to the new part of the database. (Depending on the version, your database may be in a different location. Check your MongoDB config file for dbpath option. )
sudo ln -s /block/storage/mongodb/ /var/lib/mongodb

Setting permissions
sudo chown mongodb:mongodb /block/storage/mongodb/

Start MongoDB
sudo service mongodb start

This is one method of doing it, you can also edit your MongoDB config file and set the dbpath option to block storage.