The MySQL.Data package depends on the System.Data library to create a connection directly to your database. Direct database connections are not supported by the Windows Phone libraries, since it would require your phone to connect to your databases and establish a stateful connection. These types of connections are brittle and costly to maintain.
When you browse your packages\**library**\Lib folder you'll see a binary for each supported platform. For example the HTMLAgilityPack includes a sl4-windowsphone71, and is thus supported. The MySQL.Data does not, and as such is not supported:

Instead you'll need to expose a webservice (XML or JSON for example) which can be consumed by your Windows Phone app in a stateless fashion.