The Song:

In order for it to feel more authentic, Beck filled out his Song Reader book with fragments of songs and melodies, as well as fictional album collections and made-up song titles. "The Mascot and The Magpie" is listed as part of a collection of manly hymns, Hymns For Him.

While a lot of the song titles on Hymns are made-up jokes, some are references to older sheet music/songs. I was unable to turn up what this would be a reference to exactly (or if just a joke of some sort). There is sheet music called "The Mascot" and some about magpies, but didn't see how/why they were combined.