The sheet music is at the Levy Collection (click on the title, and go on to next pages).

Title: Save My Mother's Picture. Song and Chorus.
Composer, Lyricist, Arranger: Words by C.W. Brown. Music by J. Walsh.
J. Walsh Publication: New York: Willis Woodward & Co., 842 & 844 Broadway, 1885.
Form of Composition: strophic with chorus
Instrumentation: piano and voice (solo and satb chorus)
First Line: I've been thinking of the day that has long since passed away
First Line of Chorus: My mother's face that dear old face, her loss I ever shall bewail
Engraver, Lithographer, Artist: Thorburn N.Y.
Advertisement: ads on inside front and on back covers for Willis Woodward & Co. stock
Subject: Mothers & children
Subject: Death
Subject: Grief
Subject: Auctions
Subject: Keepsakes
Call No.: Box: 138 Item: 093

Recording is:

"Save My Mother's Picture From The Sale" by Dr Smith's Champion Hoss Hair Pullers (1929) [RealAudio; melody is not the same], from Honkingduck.

~Masato