can I use homepod mini to listen to spotify?

Play audio using Siri on HomePod says you can. I don't have Spotify, so I can't verify this for you.

See under the paragraph: Play Apple Music or other music services

To add a music service to your HomePod see the task below. Once a music service is added to your HomePod try the examples below and specify which app to use. For example, say something like “Hey Siri, play Billie Eilish on Spotify.” 

You can using Airplay.