As StreamYard is browser based, it's ability to recognize and use your interface/mixer would be based on the browser's ability to do so.
1. Firstly, make sure that you are using channel 1 or 2 of the audio interface, and that your browser has permissions to access your mic devices.
2. Navigate to this mic test site and try to select and use your interface/mixer there. If you are unable to on that site as well, it may indicate a browser or device related issue.
3. Try using a different browser. (We recommend testing Google Chrome and Firefox).
4. Check to make sure the latest drivers are downloaded and updated for your device.
5. Try restarting your device, and unplugging/plugging your mixer back in.